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Theorem ax12 1881
 Description: Derive ax-12 1633 from ax-12o 1664. (Contributed by NM, 21-Dec-2015.) (New usage is discouraged.)
Assertion
Ref Expression
ax12

Proof of Theorem ax12
StepHypRef Expression
1 ax-4 1692 . . . . . 6
21con3i 129 . . . . 5
32adantr 453 . . . 4
4 equtrr 1827 . . . . . . . 8
54equcoms 1825 . . . . . . 7
65con3rr3 130 . . . . . 6
76imp 420 . . . . 5
8 ax-4 1692 . . . . 5
97, 8nsyl 115 . . . 4
10 ax-12o 1664 . . . 4
113, 9, 10sylc 58 . . 3
1211ex 425 . 2
1312pm2.43d 46 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wa 360  wal 1532 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-8 1623  ax-17 1628  ax-12o 1664  ax-9 1684  ax-4 1692 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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