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Theorem r19.26-2 2647
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 2646 . . 3  |-  ( A. y  e.  B  ( ph  /\  ps )  <->  ( A. y  e.  B  ph  /\  A. y  e.  B  ps ) )
21ralbii 2538 . 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 2646 . 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 242 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:    <-> wb 178    /\ wa 360   A.wral 2516
This theorem is referenced by:  fununi  5219  tz7.48lem  6386  isffth2  13717  ispos2  14009  isnsg2  14574  efgred  14984  dfrhm2  15425  caucfil  18636  aalioulem6  19644  ajmoi  21362  adjmo  22337  iccllyscon  23118  dfso3  23411  r19.26-2a  24265  ispridl2  25995  ishlat2  28673
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-nf 1540  df-ral 2520
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