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Theorem r19.21aivvaOLD 25750
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Moved to ralrimivva 2635 in main set.mm and may be deleted by mathbox owner, JM. --NM 17-Jul-2012.) (Contributed by Jeff Madsen, 19-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
r19.21aivva.1OLD  |-  ( (
ph  /\  ( x  e.  A  /\  y  e.  B ) )  ->  ps )
Assertion
Ref Expression
r19.21aivvaOLD  |-  ( ph  ->  A. x  e.  A  A. y  e.  B  ps )
Distinct variable groups:    ph, x, y   
y, A
Allowed substitution hints:    ps( x, y)    A( x)    B( x, y)

Proof of Theorem r19.21aivvaOLD
StepHypRef Expression
1 r19.21aivva.1OLD . 2  |-  ( (
ph  /\  ( x  e.  A  /\  y  e.  B ) )  ->  ps )
21ralrimivva 2635 1  |-  ( ph  ->  A. x  e.  A  A. y  e.  B  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358    e. wcel 1684   A.wral 2543
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-nf 1532  df-ral 2548
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