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Theorem equsalhw 1742
 Description: Weaker version of equsalh 1914 (requiring distinct variables) without using ax-12 1878. (Contributed by NM, 29-Nov-2015.)
Hypotheses
Ref Expression
equsalhw.1
equsalhw.2
Assertion
Ref Expression
equsalhw
Distinct variable group:   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem equsalhw
StepHypRef Expression
1 equsalhw.2 . . . . 5
2 sp 1728 . . . . . 6
3 equsalhw.1 . . . . . 6
42, 3impbii 180 . . . . 5
51, 4syl6bbr 254 . . . 4
65pm5.74i 236 . . 3
76albii 1556 . 2
83a1d 22 . . . 4
93, 8alrimih 1555 . . 3
10 ax9v 1645 . . . . 5
11 con3 126 . . . . . 6
1211al2imi 1551 . . . . 5
1310, 12mtoi 169 . . . 4
14 ax6o 1735 . . . 4
1513, 14syl 15 . . 3
169, 15impbii 180 . 2
177, 16bitr4i 243 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176  wal 1530 This theorem is referenced by:  dvelimhw  1747  dvelimhwNEW7  29432  equsexv-x12  29735  equveliv  29737 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
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