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Theorem ala1 1704
Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018.)
Assertion
Ref Expression
ala1  |-  ( A. x ph  ->  A. x
( ps  ->  ph )
)

Proof of Theorem ala1
StepHypRef Expression
1 ax-1 6 . 2  |-  ( ph  ->  ( ps  ->  ph )
)
21alimi 1678 1  |-  ( A. x ph  ->  A. x
( ps  ->  ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1663  ax-4 1676
This theorem is referenced by:  19.38  1706  ax12dgen  1884  stdpc4  2151  alral  2787  hbimtg  30460  bj-axdd2  31179  bj-equsal1t  31394
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