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Theorem ax12olem1 1868
 Description: Lemma for ax12o 1875. Similar to equvin 1941 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 1643 . . . . 5
2 equcomi 1646 . . . . 5
31, 2syl6 29 . . . 4
43con3and 428 . . 3
54exlimiv 1666 . 2
6 ax-17 1603 . . 3
7 ax-8 1643 . . . . . . . 8
8 equcomi 1646 . . . . . . . 8
97, 8syl6 29 . . . . . . 7
109equcoms 1651 . . . . . 6
1110com12 27 . . . . 5
1211con3d 125 . . . 4
13 equcomi 1646 . . . 4
1412, 13jctild 527 . . 3
156, 14spimeh 1722 . 2
165, 15impbii 180 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wex 1528 This theorem is referenced by:  ax12olem2  1869 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529
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