ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  r19.21be Unicode version

Theorem r19.21be 2453
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994.)
Hypothesis
Ref Expression
r19.21be.1  |-  ( ph  ->  A. x  e.  A  ps )
Assertion
Ref Expression
r19.21be  |-  A. x  e.  A  ( ph  ->  ps )

Proof of Theorem r19.21be
StepHypRef Expression
1 r19.21be.1 . . . 4  |-  ( ph  ->  A. x  e.  A  ps )
21r19.21bi 2450 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ps )
32expcom 114 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
43rgen 2417 1  |-  A. x  e.  A  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   A.wral 2349
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-gen 1379  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-ral 2354
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator