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

Theorem bj-exlimmp 12903
Description: Lemma for bj-vtoclgf 12910. (Contributed by BJ, 21-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-exlimmp.nf  |-  F/ x ps
bj-exlimmp.min  |-  ( ch 
->  ph )
Assertion
Ref Expression
bj-exlimmp  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  ->  ( E. x ch  ->  ps ) )

Proof of Theorem bj-exlimmp
StepHypRef Expression
1 nfa1 1506 . 2  |-  F/ x A. x ( ch  ->  (
ph  ->  ps ) )
2 bj-exlimmp.nf . 2  |-  F/ x ps
3 bj-exlimmp.min . . . . 5  |-  ( ch 
->  ph )
4 idd 21 . . . . 5  |-  ( ch 
->  ( ps  ->  ps ) )
53, 4embantd 56 . . . 4  |-  ( ch 
->  ( ( ph  ->  ps )  ->  ps )
)
65a2i 11 . . 3  |-  ( ( ch  ->  ( ph  ->  ps ) )  -> 
( ch  ->  ps ) )
76sps 1502 . 2  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  ->  ( ch  ->  ps ) )
81, 2, 7exlimd 1561 1  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  ->  ( E. x ch  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   F/wnf 1421   E.wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  bj-vtoclgft  12909
  Copyright terms: Public domain W3C validator