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Theorem exbid 1548
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
exbid.1  |-  F/ x ph
exbid.2  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
exbid  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )

Proof of Theorem exbid
StepHypRef Expression
1 exbid.1 . . 3  |-  F/ x ph
21nfri 1453 . 2  |-  ( ph  ->  A. x ph )
3 exbid.2 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
42, 3exbidh 1546 1  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   F/wnf 1390   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  mobid  1977  rexbida  2364  rexeqf  2547  opabbid  3851  repizf2  3944  oprabbid  5589  sscoll2  10968
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