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Theorem bj-2albi 31204
Description: Closed form of 2albii 1686. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-2albi  |-  ( A. x A. y ( ph  <->  ps )  ->  ( A. x A. y ph  <->  A. x A. y ps ) )

Proof of Theorem bj-2albi
StepHypRef Expression
1 albi 1684 . . 3  |-  ( A. y ( ph  <->  ps )  ->  ( A. y ph  <->  A. y ps ) )
21alimi 1678 . 2  |-  ( A. x A. y ( ph  <->  ps )  ->  A. x
( A. y ph  <->  A. y ps ) )
3 albi 1684 . 2  |-  ( A. x ( A. y ph 
<-> 
A. y ps )  ->  ( A. x A. y ph  <->  A. x A. y ps ) )
42, 3syl 17 1  |-  ( A. x A. y ( ph  <->  ps )  ->  ( A. x A. y ph  <->  A. x A. y ps ) )
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: (None)
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