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Theorem ax11v 1594
Description: This is a version of ax-11o 1590 when the variables are distinct. Axiom (C8) of [Monk2] p. 105. (Contributed by NM, 5-Aug-1993.) (Revised by Jim Kingdon, 15-Dec-2017.)
Assertion
Ref Expression
ax11v
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 a9e 1478 . 2
2 ax-17 1350 . . . . 5
3 ax-11 1330 . . . . 5
42, 3syl5 26 . . . 4
5 equequ2 1489 . . . . 5
65imbi1d 218 . . . . . . 7
76albidv 1591 . . . . . 6
87imbi2d 217 . . . . 5
95, 8imbi12d 221 . . . 4
104, 9mpbii 134 . . 3
1110exlimiv 1412 . 2
121, 11ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1266  wex 1313   wceq 1324
This theorem is referenced by:  equs5or  1597  sb56  1649
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 97  ax-ia2 98  ax-ia3 99  ax-5 1267  ax-gen 1269  ax-ie2 1315  ax-8 1328  ax-11 1330  ax-17 1350  ax-i9 1354
This theorem depends on definitions:  df-bi 108
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