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Theorem ax11v2-o 2280
 Description: Recovery of ax-11o 2220 from ax11v 2174 without using ax-11o 2220. The hypothesis is even weaker than ax11v 2174, with both distinct from and not occurring in . Thus, the hypothesis provides an alternate axiom that can be used in place of ax-11o 2220. (Contributed by NM, 2-Feb-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
ax11v2-o.1
Assertion
Ref Expression
ax11v2-o
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v2-o
StepHypRef Expression
1 a9ev 1669 . 2
2 ax11v2-o.1 . . . . 5
3 equequ2 1699 . . . . . . 7
43adantl 454 . . . . . 6
5 dveeq2-o 2263 . . . . . . . . 9
65imp 420 . . . . . . . 8
7 nfa1-o 2245 . . . . . . . . 9
83imbi1d 310 . . . . . . . . . 10
98sps-o 2238 . . . . . . . . 9
107, 9albid 1789 . . . . . . . 8
116, 10syl 16 . . . . . . 7
1211imbi2d 309 . . . . . 6
134, 12imbi12d 313 . . . . 5
142, 13mpbii 204 . . . 4
1514ex 425 . . 3
1615exlimdv 1647 . 2
171, 16mpi 17 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360  wal 1550  wex 1551 This theorem is referenced by:  ax11a2-o  2281 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-4 2214  ax-5o 2215  ax-6o 2216  ax-10o 2218  ax-12o 2221 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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