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Theorem exbidh 1576
Description: Formula-building rule for existential quantifier (deduction form). (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
exbidh.1  |-  ( ph  ->  A. x ph )
exbidh.2  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
exbidh  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )

Proof of Theorem exbidh
StepHypRef Expression
1 exbidh.1 . . 3  |-  ( ph  ->  A. x ph )
2 exbidh.2 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2alrimih 1428 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 exbi 1566 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( E. x ps  <->  E. x ch ) )
53, 4syl 14 1  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1312   E.wex 1451
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-ial 1497
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  exbid  1578  drex2  1693  drex1  1752  exbidv  1779  mobidh  2009
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