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Theorem ax11ev 1706
Description: Analogue to ax11v 1705 for existential quantification. (Contributed by Jim Kingdon, 9-Jan-2018.)
Assertion
Ref Expression
ax11ev
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11ev
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9e 1583 . 2
2 ax11e 1674 . . . . 5
3 ax-17 1416 . . . . . 6
4319.9h 1531 . . . . 5
52, 4syl6ib 150 . . . 4
6 equequ2 1596 . . . . 5
76anbi1d 438 . . . . . . 7
87exbidv 1703 . . . . . 6
98imbi1d 220 . . . . 5
106, 9imbi12d 223 . . . 4
115, 10mpbii 136 . . 3
1211exlimiv 1486 . 2
131, 12ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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