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Theorem ax12olem3aAUX7 29163
 Description: Lemma for ax12o 1976. Show the equivalence of an intermediate equivalent to ax12o 1976 with the conjunction of ax-12 1946 and a variant with negated equalities. (Contributed by NM, 29-Oct-2017.)
Assertion
Ref Expression
ax12olem3aAUX7

Proof of Theorem ax12olem3aAUX7
StepHypRef Expression
1 sp 1759 . . . . . 6
21con2i 114 . . . . 5
32imim1i 56 . . . 4
43imim2i 14 . . 3
5 sp 1759 . . . . . 6
65imim2i 14 . . . . 5
76con1d 118 . . . 4
87imim2i 14 . . 3
94, 8jca 519 . 2
10 con1 122 . . . . . 6
1110imim1d 71 . . . . 5
1211com12 29 . . . 4
1312imim3i 57 . . 3
1413imp 419 . 2
159, 14impbii 181 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359  wal 1546 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548
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