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Theorem r19.21be 2794
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 2791 . . 3  |-  ( (
ph  /\  x  e.  A )  ->  ps )
32expcom 425 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
43rgen 2758 1  |-  A. x  e.  A  ( ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1725   A.wral 2692
This theorem is referenced by:  bnj580  29036
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-ral 2697
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