Description: Derive ax-13 from ax-c9 and other older axioms.
This proof uses newer axioms ax-4 and ax-6 , but since these are proved from the older axioms above, this is acceptable and lets us avoid having to reprove several earlier theorems to use ax-c4 and ax-c10 . (Contributed by NM, 21-Dec-2015) (Proof modification is discouraged.) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | ax13fromc9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-c5 | ||
2 | 1 | con3i | |
3 | ax-c5 | ||
4 | 3 | con3i | |
5 | ax-c9 | ||
6 | 2 4 5 | syl2im | |
7 | ax13b | ||
8 | 6 7 | mpbir |