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Theorem equsal 2036
 Description: A useful equivalence related to substitution. (Contributed by NM, 2-Jun-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 5-Feb-2018.)
Hypotheses
Ref Expression
equsal.1
equsal.2
Assertion
Ref Expression
equsal

Proof of Theorem equsal
StepHypRef Expression
1 equsal.1 . . 3
2119.23 1910 . 2
3 equsal.2 . . . 4
43pm5.74i 245 . . 3
54albii 1640 . 2
6 ax6e 2002 . . 3
76a1bi 337 . 2
82, 5, 73bitr4i 277 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  E.wex 1612  F/wnf 1616 This theorem is referenced by:  equsalh  2037  equsex  2038  axc9lem2  2040  dvelimf  2076  sb6x  2125  sb6rf  2166  asymref2  5389  intirr  5390  fun11  5658  pm13.192  31317 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-12 1854  ax-13 1999 This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1613  df-nf 1617
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