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Theorem ax11v 1799
 Description: This is a version of ax-11o 1795 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 1674 . 2
2 ax-17 1506 . . . . 5
3 ax-11 1484 . . . . 5
42, 3syl5 32 . . . 4
5 equequ2 1689 . . . . 5
65imbi1d 230 . . . . . . 7
76albidv 1796 . . . . . 6
87imbi2d 229 . . . . 5
95, 8imbi12d 233 . . . 4
104, 9mpbii 147 . . 3
1110exlimiv 1577 . 2
121, 11ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1329   wceq 1331  wex 1468 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-17 1506  ax-i9 1510 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  equs5or  1802  sb56  1857
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