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Theorem ax13fromc9 31909
 Description: Derive ax-13 2026 from ax-c9 31895 and other older axioms. This proof uses newer axioms ax-4 1652 and ax-6 1771, 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 31889 and ax-c10 31891. (Contributed by NM, 21-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
ax13fromc9

Proof of Theorem ax13fromc9
StepHypRef Expression
1 ax-c5 31888 . . . . . 6
21con3i 135 . . . . 5
32adantr 463 . . . 4
4 equtrr 1821 . . . . . . . 8
54equcoms 1819 . . . . . . 7
65con3rr3 136 . . . . . 6
76imp 427 . . . . 5
8 ax-c5 31888 . . . . 5
97, 8nsyl 121 . . . 4
10 ax-c9 31895 . . . 4
113, 9, 10sylc 59 . . 3
1211ex 432 . 2
1312pm2.43d 47 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 367  wal 1403 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-c5 31888  ax-c9 31895 This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634 This theorem is referenced by: (None)
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