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Theorem albid 1547
Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
albid.1  |-  F/ x ph
albid.2  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
albid  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )

Proof of Theorem albid
StepHypRef Expression
1 albid.1 . . 3  |-  F/ x ph
21nfri 1453 . 2  |-  ( ph  ->  A. x ph )
3 albid.2 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
42, 3albidh 1410 1  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1283   F/wnf 1390
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  alexdc  1551  19.32dc  1610  eubid  1949  ralbida  2363  raleqf  2546  intab  3673  bdsepnft  10836  strcollnft  10937  sscoll2  10941
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