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Theorem equsex 1962
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  F/
equsex.2
Assertion
Ref Expression
equsex

Proof of Theorem equsex
StepHypRef Expression
1 exnal 1574 . 2
2 df-an 360 . . 3
32exbii 1582 . 2
4 equsex.1 . . . . 5  F/
54nfn 1793 . . . 4  F/
6 equsex.2 . . . . 5
76notbid 285 . . . 4
85, 7equsal 1960 . . 3
98con2bii 322 . 2
101, 3, 93bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wn 3   wi 4   wb 176   wa 358  wal 1540  wex 1541   F/wnf 1544
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
This theorem is referenced by:  equsexh  1963  cleljustALT  2015  sb56  2098  sb10f  2122
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