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Theorem r19.21be 2521
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 2518 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ps )
32expcom 115 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
43rgen 2483 1  |-  A. x  e.  A  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   A.wral 2414
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-gen 1425  ax-4 1487
This theorem depends on definitions:  df-bi 116  df-ral 2419
This theorem is referenced by: (None)
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