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Theorem equsex 2038
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 484 . . 3
41, 3exlimi 1912 . 2
51, 2equsal 2036 . . 3
6 equs4 2035 . . 3
75, 6sylbir 213 . 2
84, 7impbii 188 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  E.wex 1612  F/wnf 1616
This theorem is referenced by:  equsexh  2039  cleljustALT  2110  sb5rf  2165  sb56  2172  sb10f  2200  axsep  4572  dprd2d2  17093
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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