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Theorem ax11v 1705
Description: This is a version of ax-11o 1701 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 1583 . 2
2 ax-17 1416 . . . . 5
3 ax-11 1394 . . . . 5
42, 3syl5 28 . . . 4
5 equequ2 1596 . . . . 5
65imbi1d 220 . . . . . . 7
76albidv 1702 . . . . . 6
87imbi2d 219 . . . . 5
95, 8imbi12d 223 . . . 4
104, 9mpbii 136 . . 3
1110exlimiv 1486 . 2
121, 11ax-mp 7 1
Colors of variables: wff set class
Syntax hints:   wi 4  wal 1240   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-ie2 1380  ax-8 1392  ax-11 1394  ax-17 1416  ax-i9 1420
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  equs5or  1708  sb56  1762
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