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Theorem ax11v2 1717
 Description: Recovery of ax11o 1719 from ax11v 1724 without using ax-11 1413. The hypothesis is even weaker than ax11v 1724, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1719. (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 1602 . 2
2 ax11v2.1 . . . . 5
3 equequ2 1615 . . . . . . 7
43adantl 266 . . . . . 6
5 dveeq2 1712 . . . . . . . . 9
65imp 119 . . . . . . . 8
7 hba1 1449 . . . . . . . . 9
83imbi1d 224 . . . . . . . . . 10
98sps 1446 . . . . . . . . 9
107, 9albidh 1385 . . . . . . . 8
116, 10syl 14 . . . . . . 7
1211imbi2d 223 . . . . . 6
134, 12imbi12d 227 . . . . 5
142, 13mpbii 140 . . . 4
1514ex 112 . . 3
1615exlimdv 1716 . 2
171, 16mpi 15 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 101   wb 102  wal 1257  wex 1397 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662 This theorem is referenced by:  ax11a2  1718
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