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Theorem albidh 1720
Description: Formula-building rule for universal quantifier (deduction rule). (Contributed by NM, 26-May-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 1687 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 albi 1684 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( A. x ps  <->  A. x ch ) )
53, 4syl 17 1  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676
This theorem depends on definitions:  df-bi 188
This theorem is referenced by:  albidv  1761  albid  1940  dral2-o  32413  ax12indalem  32428  ax12inda2ALT  32429  ax12inda  32431
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