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Theorem bj-ala1 33579
Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018.) Proof modification is discouraged only to avoid using bj-ala1BIS 33554. (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ala1  |-  ( A. x ph  ->  A. x
( ps  ->  ph )
)

Proof of Theorem bj-ala1
StepHypRef Expression
1 ax-1 6 . 2  |-  ( ph  ->  ( ps  ->  ph )
)
21alimi 1614 1  |-  ( A. x ph  ->  A. x
( ps  ->  ph )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1377
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-gen 1601  ax-4 1612
This theorem is referenced by:  bj-equsal1t  33769
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