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Theorem exbidh 1644
Description: Formula-building rule for existential quantifier (deduction rule). (Contributed by NM, 26-May-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 1613 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 exbi 1634 . 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 setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by:  exbidv  1681  exbid  1825  drex2  2030  ac6s6  29133
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