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Theorem bj-alrimhi 34614
Description: An inference associated with bj-alrimh 34609 and bj-exlimh 34612. (Contributed by BJ, 12-May-2019.)
Hypothesis
Ref Expression
bj-alrimhi.1  |-  ( ph  ->  ps )
Assertion
Ref Expression
bj-alrimhi  |-  (FF/ x
ph  ->  ( E. x ph  ->  A. x ps )
)

Proof of Theorem bj-alrimhi
StepHypRef Expression
1 df-bj-nf 34596 . . 3  |-  (FF/ x
ph 
<->  ( E. x ph  ->  A. x ph )
)
21biimpi 194 . 2  |-  (FF/ x
ph  ->  ( E. x ph  ->  A. x ph )
)
3 bj-alrimhi.1 . . 3  |-  ( ph  ->  ps )
43alimi 1638 . 2  |-  ( A. x ph  ->  A. x ps )
52, 4syl6 33 1  |-  (FF/ x
ph  ->  ( E. x ph  ->  A. x ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396   E.wex 1617  FF/wnff 34595
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-bj-nf 34596
This theorem is referenced by: (None)
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