ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.36i Unicode version

Theorem 19.36i 1660
Description: Inference from Theorem 19.36 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 2-Feb-2015.)
Hypotheses
Ref Expression
19.36i.1  |-  F/ x ps
19.36i.2  |-  E. x
( ph  ->  ps )
Assertion
Ref Expression
19.36i  |-  ( A. x ph  ->  ps )

Proof of Theorem 19.36i
StepHypRef Expression
1 19.36i.2 . . 3  |-  E. x
( ph  ->  ps )
2119.35i 1613 . 2  |-  ( A. x ph  ->  E. x ps )
3 19.36i.1 . . 3  |-  F/ x ps
4 id 19 . . 3  |-  ( ps 
->  ps )
53, 4exlimi 1582 . 2  |-  ( E. x ps  ->  ps )
62, 5syl 14 1  |-  ( A. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1341   F/wnf 1448   E.wex 1480
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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-4 1498  ax-ial 1522
This theorem depends on definitions:  df-bi 116  df-nf 1449
This theorem is referenced by:  spimfv  1687  19.36aiv  1889  vtoclf  2779
  Copyright terms: Public domain W3C validator