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Theorem ax11v2 1698
Description: Recovery of ax11o 1700 from ax11v 1705 without using ax-11 1394. The hypothesis is even weaker than ax11v 1705, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1700. (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 1583 . 2
2 ax11v2.1 . . . . 5
3 equequ2 1596 . . . . . . 7
43adantl 262 . . . . . 6
5 dveeq2 1693 . . . . . . . . 9
65imp 115 . . . . . . . 8
7 hba1 1430 . . . . . . . . 9
83imbi1d 220 . . . . . . . . . 10
98sps 1427 . . . . . . . . 9
107, 9albidh 1366 . . . . . . . 8
116, 10syl 14 . . . . . . 7
1211imbi2d 219 . . . . . 6
134, 12imbi12d 223 . . . . 5
142, 13mpbii 136 . . . 4
1514ex 108 . . 3
1615exlimdv 1697 . 2
171, 16mpi 15 1
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   wb 98  wal 1240  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-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643
This theorem is referenced by:  ax11a2  1699
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