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Theorem rspec2 2797
Description: Specialization rule for restricted quantification. (Contributed by NM, 20-Nov-1994.)
Hypothesis
Ref Expression
rspec2.1  |-  A. x  e.  A  A. y  e.  B  ph
Assertion
Ref Expression
rspec2  |-  ( ( x  e.  A  /\  y  e.  B )  ->  ph )

Proof of Theorem rspec2
StepHypRef Expression
1 rspec2.1 . . 3  |-  A. x  e.  A  A. y  e.  B  ph
21rspec 2762 . 2  |-  ( x  e.  A  ->  A. y  e.  B  ph )
32r19.21bi 2796 1  |-  ( ( x  e.  A  /\  y  e.  B )  ->  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359    e. wcel 1725   A.wral 2697
This theorem is referenced by:  rspec3  2798
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 2702
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