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Theorem rsp2 2388
Description: Restricted specialization. (Contributed by NM, 11-Feb-1997.)
Assertion
Ref Expression
rsp2  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  ( ( x  e.  A  /\  y  e.  B
)  ->  ph ) )

Proof of Theorem rsp2
StepHypRef Expression
1 rsp 2386 . . 3  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  ( x  e.  A  ->  A. y  e.  B  ph ) )
2 rsp 2386 . . 3  |-  ( A. y  e.  B  ph  ->  ( y  e.  B  ->  ph ) )
31, 2syl6 33 . 2  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  ( x  e.  A  -> 
( y  e.  B  ->  ph ) ) )
43impd 246 1  |-  ( A. x  e.  A  A. y  e.  B  ph  ->  ( ( x  e.  A  /\  y  e.  B
)  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    e. wcel 1409   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-4 1416
This theorem depends on definitions:  df-bi 114  df-ral 2328
This theorem is referenced by:  ralidm  3349  sowlin  4085
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