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Theorem bj-exlimmpbi 31506
Description: Lemma for theorems of the vtoclg 3106 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpbi.nf  |-  F/ x ps
bj-exlimmpbi.maj  |-  ( ch 
->  ( ph  <->  ps )
)
bj-exlimmpbi.min  |-  ph
Assertion
Ref Expression
bj-exlimmpbi  |-  ( E. x ch  ->  ps )

Proof of Theorem bj-exlimmpbi
StepHypRef Expression
1 bj-exlimmpbi.nf . 2  |-  F/ x ps
2 bj-exlimmpbi.min . . 3  |-  ph
3 bj-exlimmpbi.maj . . 3  |-  ( ch 
->  ( ph  <->  ps )
)
42, 3mpbii 215 . 2  |-  ( ch 
->  ps )
51, 4exlimi 1994 1  |-  ( E. x ch  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 188   E.wex 1662   F/wnf 1666
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-12 1932
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1663  df-nf 1667
This theorem is referenced by: (None)
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