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Theorem ax12 1935
 Description: Derive ax-12 1925 from ax12v 1926 via ax12o 1934. This shows that the weakening in ax12v 1926 is still sufficient for a complete system. (Contributed by NM, 21-Dec-2015.)
Assertion
Ref Expression
ax12

Proof of Theorem ax12
StepHypRef Expression
1 sp 1747 . . . . . 6
21con3i 127 . . . . 5
32adantr 451 . . . 4
4 equtrr 1683 . . . . . . . 8
54equcoms 1681 . . . . . . 7
65con3rr3 128 . . . . . 6
76imp 418 . . . . 5
8 sp 1747 . . . . 5
97, 8nsyl 113 . . . 4
10 ax12o 1934 . . . 4
113, 9, 10sylc 56 . . 3
1211ex 423 . 2
1312pm2.43d 44 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358  wal 1540 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545 This theorem is referenced by: (None)
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