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Theorem ax11v2 2048
 Description: Recovery of ax-11o 2195 from ax11v 2149. This proof uses ax-10 2194 and ax-11 1757. TODO: figure out if this is useful, or if it should be simplified or eliminated. (Contributed by NM, 2-Feb-2007.) (Proof shortened by Wolf Lammen, 21-Apr-2018.)
Hypothesis
Ref Expression
ax11v2.1
Assertion
Ref Expression
ax11v2
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem ax11v2
StepHypRef Expression
1 a9ev 1664 . 2
2 dveeq2 2022 . . . 4
3 ax11v2.1 . . . . 5
4 equequ2 1694 . . . . . . 7
54sps 1766 . . . . . 6
6 nfa1 1802 . . . . . . . 8
75imbi1d 309 . . . . . . . 8
86, 7albid 1784 . . . . . . 7
98imbi2d 308 . . . . . 6
105, 9imbi12d 312 . . . . 5
113, 10mpbii 203 . . . 4
122, 11syl6 31 . . 3
1312exlimdv 1643 . 2
141, 13mpi 17 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177  wal 1546  wex 1547 This theorem is referenced by:  ax11a2  2050 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551
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