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Theorem equsex 2003
 Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.) (Proof shortened by Wolf Lammen, 6-Feb-2018.)
Hypotheses
Ref Expression
equsex.1
equsex.2
Assertion
Ref Expression
equsex

Proof of Theorem equsex
StepHypRef Expression
1 equsex.1 . . 3
2 equsex.2 . . . 4
32biimpa 472 . . 3
41, 3exlimi 1822 . 2
51, 2equsal 2000 . . 3
6 equs4 1998 . . 3
75, 6sylbir 206 . 2
84, 7impbii 182 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550  wex 1551  wnf 1554 This theorem is referenced by:  equsexh  2005  cleljustALT  2106  sb56  2176  sb10f  2201  axsep  4331  dprd2d2  15604 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762  ax-12 1951 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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