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Theorem cbv3hv 1737
 Description: Lemma for ax10 1884. Similar to cbv3h 1923. Requires distinct variables but avoids ax-12 1866. (Contributed by NM, 25-Jul-2015.)
Hypotheses
Ref Expression
cbv3hv.1
cbv3hv.2
cbv3hv.3
Assertion
Ref Expression
cbv3hv
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbv3hv
StepHypRef Expression
1 cbv3hv.1 . . 3
21alimi 1546 . 2
3 ax9v 1636 . . . . 5
4 hba1 1719 . . . . . . . 8
5 cbv3hv.2 . . . . . . . 8
64, 5hbim 1725 . . . . . . 7
76hbn 1720 . . . . . 6
8 sp 1716 . . . . . . . 8
9 cbv3hv.3 . . . . . . . 8
108, 9syl5 28 . . . . . . 7
1110con3i 127 . . . . . 6
127, 11alrimih 1552 . . . . 5
133, 12mt3 171 . . . 4
1413alimi 1546 . . 3
1514a7s 1709 . 2
162, 15syl 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4  wal 1527 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-7 1708  ax-11 1715
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