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Full Idea
A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism.
Gist of Idea
Supposing axioms (rather than accepting them) give truths, but they are conditional
Source
Michael Potter (Set Theory and Its Philosophy [2004], 01.1)
Book Ref
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.8
A Reaction
Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth).