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Theorem ax11v 1569
Description: This is a version of ax-11o 1491 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 1389 . 2
2 ax-17 1280 . . . . 5
3 ax-11 1268 . . . . 5
42, 3syl5 26 . . . 4
5 equequ2 1401 . . . . 5
65imbi1d 218 . . . . . . 7
76albidv 1550 . . . . . 6
87imbi2d 217 . . . . 5
95, 8imbi12d 221 . . . 4
104, 9mpbii 134 . . 3
1110exlimiv 1568 . 2
121, 11ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1214  wex 1253   wceq 1262
This theorem is referenced by:  sb56  1571
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 1215  ax-gen 1218  ax-ie2 1255  ax-8 1266  ax-11 1268  ax-17 1280  ax-i9 1282
This theorem depends on definitions:  df-bi 108
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