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Theorem equsexv-x12 29735
 Description: Weaker version of equsex 1915 without using sp 1728, ax9 1902, ax10 1897, or ax12o but allowing ax9v 1645. Experiment to study ax12o 1887. (Contributed by NM, 7-Nov-1015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
equsexv-x12.1
equsexv-x12.2
Assertion
Ref Expression
equsexv-x12
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem equsexv-x12
StepHypRef Expression
1 exnal 1564 . 2
2 df-an 360 . . 3
32exbii 1572 . 2
4 equsexv-x12.1 . . . . 5
54hbn 1732 . . . 4
6 equsexv-x12.2 . . . . 5
76notbid 285 . . . 4
85, 7equsalhw 1742 . . 3
98con2bii 322 . 2
101, 3, 93bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1530  wex 1531 This theorem is referenced by:  equvinv  29736 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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