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Theorem equsal 1999
 Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-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 1819 . 2
3 equsal.2 . . . 4
43pm5.74i 237 . . 3
54albii 1575 . 2
6 a9e 1952 . . 3
76a1bi 328 . 2
82, 5, 73bitr4i 269 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550  wnf 1553 This theorem is referenced by:  equsalh  2001  equsex  2002  equsexOLD  2003  dvelimf  2068  dvelimfOLD  2069  sb6x  2121  asymref2  5251  intirr  5252  fun11  5516  pm13.192  27587 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-12 1950 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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