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Theorem r19.26-2 2599
Description: Theorem 19.26 of [Margaris] p. 90 with 2 restricted quantifiers. (Contributed by NM, 10-Aug-2004.)
Assertion
Ref Expression
r19.26-2  |-  ( A. x  e.  A  A. y  e.  B  ( ph  /\  ps )  <->  ( A. x  e.  A  A. y  e.  B  ph  /\  A. x  e.  A  A. y  e.  B  ps ) )

Proof of Theorem r19.26-2
StepHypRef Expression
1 r19.26 2596 . . 3  |-  ( A. y  e.  B  ( ph  /\  ps )  <->  ( A. y  e.  B  ph  /\  A. y  e.  B  ps ) )
21ralbii 2476 . 2  |-  ( A. x  e.  A  A. y  e.  B  ( ph  /\  ps )  <->  A. x  e.  A  ( A. y  e.  B  ph  /\  A. y  e.  B  ps ) )
3 r19.26 2596 . 2  |-  ( A. x  e.  A  ( A. y  e.  B  ph 
/\  A. y  e.  B  ps )  <->  ( A. x  e.  A  A. y  e.  B  ph  /\  A. x  e.  A  A. y  e.  B  ps ) )
42, 3bitri 183 1  |-  ( A. x  e.  A  A. y  e.  B  ( ph  /\  ps )  <->  ( A. x  e.  A  A. y  e.  B  ph  /\  A. x  e.  A  A. y  e.  B  ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   A.wral 2448
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-5 1440  ax-gen 1442  ax-4 1503  ax-17 1519
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-ral 2453
This theorem is referenced by:  fununi  5264  issgrpv  12631  issgrpn0  12632
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