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Theorem exbidh 1598
Description: Formula-building rule for existential quantifier (deduction rule). (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 1571 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 exbi 1588 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( E. x ps  <->  E. x ch ) )
53, 4syl 16 1  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177   A.wal 1546   E.wex 1547
This theorem is referenced by:  exbidv  1633  exbid  1781  drex2  2007  drex2wAUX7  28835  drex2w2AUX7  28838  drex2OLD7  29031
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563
This theorem depends on definitions:  df-bi 178  df-ex 1548
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