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

Theorem bj-exlimmpi 33433
Description: Lemma for bj-vtoclg1f1 33438 (an instance of this lemma is a version of bj-vtoclg1f1 33438 where  x and  y are identified). (Contributed by BJ, 30-Apr-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmpi.nf  |-  F/ x ps
bj-exlimmpi.maj  |-  ( ch 
->  ( ph  ->  ps ) )
bj-exlimmpi.min  |-  ph
Assertion
Ref Expression
bj-exlimmpi  |-  ( E. x ch  ->  ps )

Proof of Theorem bj-exlimmpi
StepHypRef Expression
1 bj-exlimmpi.nf . 2  |-  F/ x ps
2 bj-exlimmpi.min . . 3  |-  ph
3 bj-exlimmpi.maj . . 3  |-  ( ch 
->  ( ph  ->  ps ) )
42, 3mpi 17 . 2  |-  ( ch 
->  ps )
51, 4exlimi 1854 1  |-  ( E. x ch  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1591   F/wnf 1594
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-12 1798
This theorem depends on definitions:  df-bi 185  df-ex 1592  df-nf 1595
This theorem is referenced by:  bj-vtoclg1f1  33438  bj-vtoclg1f  33439  bj-vtoclg1fv  33440
  Copyright terms: Public domain W3C validator