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Theorem ax7w9AUX7 29834
 Description: Special case of ax-7 1752 proved from ax-7v 29616. (Contributed by NM, 28-Nov-2017.)
Assertion
Ref Expression
ax7w9AUX7

Proof of Theorem ax7w9AUX7
StepHypRef Expression
1 equcomi 1694 . . . . . . 7
21adantr 453 . . . . . 6
3 ax-8 1690 . . . . . . 7
43imp 420 . . . . . 6
52, 4jca 520 . . . . 5
65alimi 1569 . . . 4
7 19.26 1605 . . . . 5
8 aecomNEW7 29648 . . . . . . . 8
9 hbaew0AUX7 29821 . . . . . . . 8
108, 9anim12i 551 . . . . . . 7
11 19.26 1605 . . . . . . 7
1210, 11sylibr 205 . . . . . 6
13 equtr 1697 . . . . . . . 8
1413imdistani 673 . . . . . . 7
1514alimi 1569 . . . . . 6
1612, 15syl 16 . . . . 5
177, 16sylbi 189 . . . 4
186, 17syl 16 . . 3
1918a5i 1810 . 2
2019sps 1773 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360  wal 1550 This theorem is referenced by:  alcomw9bAUX7  29835 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-11 1764  ax-12 1954  ax-7v 29616 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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