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Theorem albid 1594
Description: Formula-building rule for universal quantifier (deduction form). (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 1499 . 2  |-  ( ph  ->  A. x ph )
3 albid.2 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
42, 3albidh 1456 1  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104   A.wal 1329   F/wnf 1436
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 1423  ax-gen 1425  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  alexdc  1598  19.32dc  1657  eubid  2006  ralbida  2431  raleqf  2622  intab  3800  bdsepnft  13115  strcollnft  13212  sscoll2  13216
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