The Buddha teaches that whether a Buddha arises or not, existence arises as a consequence of a chain of interdependent factors, that each of the factors is impermanent, and that one who sees coming into existence and existence in this way will not have ideas of self with regard to the past, future or present.
Read the Sutta
Index of Available translations: SN 2.12.20
A famous sutta because of the following lines:
Uppaadaa vaa Tathaagataana.m||
anuppaadaa vaa Tathaagataana.m||
.thitaa va saa dhaatu||
or Tathaagatas not appearing,
one fact remains:
things are established
things are steered
- Olds, trans.
Mrs. Rhys Davids:
Whether, brethren, there be an arising of Tathaagatas,
or whether there be no such arising,
this nature of things just stands,
this causal status,
this causal orderliness,
the relatedness of this to that.
Whether or not there is the arising of Tathaagatas,
this property stands -
this regularity of the Dhamma,
this orderliness of the Dhamma,
this this/that conditionality.
Whethere there is an arising of Tathaagatas,
or no arising of Tathaagatas,
that element still persists,
the stableness of the Dhamma,
the fixed course of the Dhamma,
Obviously the saying is famous not because there is any agreement as to what it means, but because of the statement that the phenomena of dependence is something that was discovered by the Buddha, not invented by him, and is, consequently, discoverable by others for themselves. An idea that is always appealing to the rational mind.
I have changed my attitude towards translating 'dhaatu' as 'element'. Thought of as 'aspect', as it could be here, it would be a useful translation. But note my use of 'fact' as a translation for 'dhaatu'. which works very well here. I have not seen this used before for 'dhaatu' and it seems to reasonably fit most cases.
I don't think translating 'dhamma' here as 'Dhamma' makes good sense. This is speaking about something that is possible to discover without the appearance of a Buddha. If 'the teaching' is intended by 'Dhamma' that is out of the question in this case.
It is possible that this refers to 'a law of nature' (such as the Tao) but that would throw the meaning of the sutta from the discussion of 'this resulting from that' to the nature of Dhamma.
And it would do it for only this section, where, if it were a discussion of Dhamma as a law of nature, this idea should be present in the next two sections.
I think the simpler explanation is that Gotama is explaining how things work whether or not Buddhas appear.
As for the obscurity of the last line, I believe that is answered by understanding that in many cases like this when the word 'this' is used, it is intended to mean 'this world' or 'this that has become' or 'this body' or 'this everything whatsoever'.
See on this idea the use of 'this' in the definition of 'dukkha' at DN 22 and elsewhere, 'Ida.m dukkhan.' and in the next sutta in the condensed version of the pa.ticca samuppada: Iti imasmi.m sati ida.m hoti.
The idea is basically as the other translators have it: [~ is the case] through this resulting in that. The idea seems to have been understood in the condensed formula something like I have given it.