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Theorem equsalhw 1838
 Description: Weaker version of equsalh 1961 (requiring distinct variables) without using ax-12 1925. (Contributed by NM, 29-Nov-2015.) (Proof shortened by Wolf Lammen, 28-Dec-2017.)
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.1 . . 3
2119.23h 1802 . 2
3 equsalhw.2 . . . 4
43pm5.74i 236 . . 3
54albii 1566 . 2
6 a9ev 1656 . . 3
76a1bi 327 . 2
82, 5, 73bitr4i 268 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  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-11 1746 This theorem depends on definitions:  df-bi 177  df-ex 1542  df-nf 1545 This theorem is referenced by:  dvelimhw  1849
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