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Theorem albidh 1441
Description: Formula-building rule for universal quantifier (deduction form). (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
albidh.1  |-  ( ph  ->  A. x ph )
albidh.2  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
albidh  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )

Proof of Theorem albidh
StepHypRef Expression
1 albidh.1 . . 3  |-  ( ph  ->  A. x ph )
2 albidh.2 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2alrimih 1430 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 albi 1429 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( A. x ps  <->  A. x ch ) )
53, 4syl 14 1  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1314
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 1408  ax-gen 1410
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nfbidf  1504  albid  1579  dral2  1694  ax11v2  1776  albidv  1780  equs5or  1786  sbal2  1975  eubidh  1983
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