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Theorem ax11v2 1651
Description: Recovery of ax11o 1653 from ax11v 1703 without using ax-11 1389. The hypothesis is even weaker than ax11v 1703, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1653.
Hypothesis
Ref Expression
ax11v2.1
Assertion
Ref Expression
ax11v2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v2
StepHypRef Expression
1 a9e 1556 . 2
2 ax11v2.1 . . . . 5
3 equequ2 1571 . . . . . . 7
43adantl 261 . . . . . 6
5 dveeq2 1646 . . . . . . . . 9
65imp 114 . . . . . . . 8
7 hba1 1436 . . . . . . . . 9
83imbi1d 219 . . . . . . . . . 10
98a4s 1433 . . . . . . . . 9
107, 9albid 1360 . . . . . . . 8
116, 10syl 14 . . . . . . 7
1211imbi2d 218 . . . . . 6
134, 12imbi12d 222 . . . . 5
142, 13mpbii 135 . . . 4
1514ex 107 . . 3
1615exlimdv 1650 . 2
171, 16mpi 15 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 96   wb 97  wal 1335  wex 1374
This theorem is referenced by:  ax11a2  1652
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-ia1 98  ax-ia2 99  ax-ia3 100  ax-in1 527  ax-in2 528  ax-io 607  ax-5 1336  ax-6 1337  ax-7 1338  ax-gen 1339  ax-ie1 1375  ax-ie2 1376  ax-8 1387  ax-10 1388  ax-11 1389  ax-i12 1391  ax-4 1392  ax-17 1402  ax-i9 1417  ax-ial 1430  ax-i5r 1431
This theorem depends on definitions:  df-bi 109
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