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Theorem exbid 1507
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 1412 . 2  |-  ( ph  ->  A. x ph )
3 exbid.2 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
42, 3exbidh 1505 1  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   F/wnf 1349   E.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-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by:  mobid  1935  rexbida  2318  rexeqf  2499  opabbid  3819  repizf2  3912  oprabbid  5545  sscoll2  9986
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