Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bj-exlimmpbir Structured version   Visualization version   Unicode version

Theorem bj-exlimmpbir 31507
Description: Lemma for theorems of the vtoclg 3106 family. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpbir.nf  |-  F/ x ph
bj-exlimmpbir.maj  |-  ( ch 
->  ( ph  <->  ps )
)
bj-exlimmpbir.min  |-  ps
Assertion
Ref Expression
bj-exlimmpbir  |-  ( E. x ch  ->  ph )

Proof of Theorem bj-exlimmpbir
StepHypRef Expression
1 bj-exlimmpbir.nf . 2  |-  F/ x ph
2 bj-exlimmpbir.min . . 3  |-  ps
3 bj-exlimmpbir.maj . . 3  |-  ( ch 
->  ( ph  <->  ps )
)
42, 3mpbiri 237 . 2  |-  ( ch 
->  ph )
51, 4exlimi 1994 1  |-  ( E. x ch  ->  ph )
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)
  Copyright terms: Public domain W3C validator