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Theorem ax12olem1 1880
 Description: Lemma for ax12o 1887. Similar to equvin 1954 but with a negated equality. (Contributed by NM, 24-Dec-2015.)
Assertion
Ref Expression
ax12olem1
Distinct variable groups:   ,   ,

Proof of Theorem ax12olem1
StepHypRef Expression
1 ax-8 1661 . . . . 5
2 equcomi 1664 . . . . 5
31, 2syl6 29 . . . 4
43con3and 428 . . 3
54exlimiv 1624 . 2
6 ax-17 1606 . . 3
7 ax-8 1661 . . . . . . . 8
8 equcomi 1664 . . . . . . . 8
97, 8syl6 29 . . . . . . 7
109equcoms 1666 . . . . . 6
1110com12 27 . . . . 5
1211con3d 125 . . . 4
13 equcomi 1664 . . . 4
1412, 13jctild 527 . . 3
156, 14spimeh 1734 . 2
165, 15impbii 180 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wex 1531 This theorem is referenced by:  ax12olem2  1881  ax12olem2wAUX7  29432  ax12olem2OLD7  29660 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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