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Theorem bj-hbxfrbi 31215
Description: Closed form of hbxfrbi 1688. Notes: it is less important than bj-nfbi 31216; it requires sp 1914 (unlike bj-nfbi 31216); there is an obvious version with  ( E. x ph  ->  ph ) instead. (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-hbxfrbi  |-  ( A. x ( ph  <->  ps )  ->  ( ( ph  ->  A. x ph )  <->  ( ps  ->  A. x ps )
) )

Proof of Theorem bj-hbxfrbi
StepHypRef Expression
1 sp 1914 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( ph  <->  ps )
)
2 albi 1684 . 2  |-  ( A. x ( ph  <->  ps )  ->  ( A. x ph  <->  A. x ps ) )
31, 2imbi12d 321 1  |-  ( A. x ( ph  <->  ps )  ->  ( ( ph  ->  A. x ph )  <->  ( ps  ->  A. x 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  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658
This theorem is referenced by: (None)
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