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Theorem albidh 1580
Description: Formula-building rule for universal quantifier (deduction rule). (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 1555 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 albi 1554 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( A. x ps  <->  A. x ch ) )
53, 4syl 15 1  |-  ( ph  ->  ( A. x ps  <->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   A.wal 1530
This theorem is referenced by:  albidv  1615  albid  1764  ax10lem4  1894  ax9  1902  dral2  1919  dral2-o  2133  ax11indalem  2149  ax11inda2ALT  2150  ax11inda  2152  ax9NEW7  29445  ax10lem4NEW7  29448  dral2wAUX7  29473  dral2w2AUX7  29476  dral2OLD7  29668  ax10lem18ALT  29746
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177
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