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Theorem ax13fromc9 2235
 Description: Derive ax-13 1999 from ax-c9 2221 and other older axioms. This proof uses newer axioms ax-4 1631 and ax-6 1747, 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 2215 and ax-c10 2217. (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 2214 . . . . . 6
21con3i 135 . . . . 5
32adantr 465 . . . 4
4 equtrr 1797 . . . . . . . 8
54equcoms 1795 . . . . . . 7
65con3rr3 136 . . . . . 6
76imp 429 . . . . 5
8 ax-c5 2214 . . . . 5
97, 8nsyl 121 . . . 4
10 ax-c9 2221 . . . 4
113, 9, 10sylc 60 . . 3
1211ex 434 . 2
1312pm2.43d 48 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-c5 2214  ax-c9 2221 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613
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