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

Theorem bj-exlimmp 10840
Description: Lemma for bj-vtoclgf 10846. (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 1475 . 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 55 . . . 4  |-  ( ch 
->  ( ( ph  ->  ps )  ->  ps )
)
65a2i 11 . . 3  |-  ( ( ch  ->  ( ph  ->  ps ) )  -> 
( ch  ->  ps ) )
76sps 1471 . 2  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  ->  ( ch  ->  ps ) )
81, 2, 7exlimd 1529 1  |-  ( A. x ( ch  ->  (
ph  ->  ps ) )  ->  ( E. x ch  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1283   F/wnf 1390   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  bj-vtoclgft  10845
  Copyright terms: Public domain W3C validator