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Theorem equsex 1616
 Description: A useful equivalence related to substitution. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.)
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 280 . . 3
41, 3exlimih 1484 . 2
5 a9e 1586 . . 3
6 idd 21 . . . . 5
72biimprcd 149 . . . . 5
86, 7jcad 291 . . . 4
91, 8eximdh 1502 . . 3
105, 9mpi 15 . 2
114, 10impbii 117 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241   wceq 1243  wex 1381 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-i9 1423  ax-ial 1427 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  cbvexh  1638  sb56  1765  cleljust  1813  sb10f  1871
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