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Theorem ax11v2-o 2201
 Description: Recovery of ax-11o 2141 from ax11v 2096 without using ax-11o 2141. The hypothesis is even weaker than ax11v 2096, with both distinct from and not occurring in . Thus, the hypothesis provides an alternate axiom that can be used in place of ax-11o 2141. (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 1656 . 2
2 ax11v2-o.1 . . . . 5
3 equequ2 1686 . . . . . . 7
43adantl 452 . . . . . 6
5 dveeq2-o 2184 . . . . . . . . 9
65imp 418 . . . . . . . 8
7 nfa1-o 2166 . . . . . . . . 9
83imbi1d 308 . . . . . . . . . 10
98sps-o 2159 . . . . . . . . 9
107, 9albid 1772 . . . . . . . 8
116, 10syl 15 . . . . . . 7
1211imbi2d 307 . . . . . 6
134, 12imbi12d 311 . . . . 5
142, 13mpbii 202 . . . 4
1514ex 423 . . 3
1615exlimdv 1636 . 2
171, 16mpi 16 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540  wex 1541 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-4 2135  ax-5o 2136  ax-6o 2137  ax-10o 2139  ax-12o 2142 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545 This theorem is referenced by:  ax11a2-o  2202
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