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Theorem equsex 1915
 Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 3-Oct-2016.)
Hypotheses
Ref Expression
equsex.1
equsex.2
Assertion
Ref Expression
equsex

Proof of Theorem equsex
StepHypRef Expression
1 exnal 1564 . 2
2 df-an 360 . . 3
32exbii 1572 . 2
4 equsex.1 . . . . 5
54nfn 1777 . . . 4
6 equsex.2 . . . . 5
76notbid 285 . . . 4
85, 7equsal 1913 . . 3
98con2bii 322 . 2
101, 3, 93bitr4i 268 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1530  wex 1531  wnf 1534 This theorem is referenced by:  equsexh  1916  cleljustALT  1968  sb56  2050  sb10f  2074  axsep  4156 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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