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Theorem ax11v2 1587
Description: Recovery of ax11o 1589 from ax11v 1594 without using ax-11 1330. The hypothesis is even weaker than ax11v 1594, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1589. (Contributed by NM, 2-Feb-2007.)
Hypothesis
Ref Expression
ax11v2.1
Assertion
Ref Expression
ax11v2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v2
StepHypRef Expression
1 a9e 1478 . 2
2 ax11v2.1 . . . . 5
3 equequ2 1489 . . . . . . 7
43adantl 260 . . . . . 6
5 dveeq2 1582 . . . . . . . . 9
65imp 113 . . . . . . . 8
7 hba1 1365 . . . . . . . . 9
83imbi1d 218 . . . . . . . . . 10
98a4s 1362 . . . . . . . . 9
107, 9albid 1299 . . . . . . . 8
116, 10syl 13 . . . . . . 7
1211imbi2d 217 . . . . . 6
134, 12imbi12d 221 . . . . 5
142, 13mpbii 134 . . . 4
1514ex 106 . . 3
1615exlimdv 1586 . 2
171, 16mpi 14 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 95   wb 96  wal 1266  wex 1313
This theorem is referenced by:  ax11a2  1588
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-in2 528  ax-io 609  ax-5 1267  ax-7 1268  ax-gen 1269  ax-ie1 1314  ax-ie2 1315  ax-8 1328  ax-10 1329  ax-11 1330  ax-i12 1331  ax-4 1333  ax-17 1350  ax-i9 1354  ax-ial 1359
This theorem depends on definitions:  df-bi 108  df-sb 1533
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