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Theorem bj-axc15v 34431
 Description: Version of axc15 2086 with a dv condition, which does not require ax-13 2000. (Contributed by BJ, 14-Jun-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-axc15v
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem bj-axc15v
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax6ev 1750 . 2
2 ax5d 1706 . . . 4
3 ax-5 1705 . . . . . 6
4 ax-12 1855 . . . . . 6
53, 4syl5 32 . . . . 5
6 equequ2 1800 . . . . . . 7
76sps 1866 . . . . . 6
8 nfa1 1898 . . . . . . . 8
97imbi1d 317 . . . . . . . 8
108, 9albid 1886 . . . . . . 7
1110imbi2d 316 . . . . . 6
127, 11imbi12d 320 . . . . 5
135, 12mpbii 211 . . . 4
142, 13syl6 33 . . 3
1514exlimdv 1725 . 2
161, 15mpi 17 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184  wal 1393  wex 1613 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-10 1838  ax-12 1855 This theorem depends on definitions:  df-bi 185  df-ex 1614  df-nf 1618 This theorem is referenced by:  bj-equs5v  34433  bj-ax12v  34449
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