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Theorem r19.26-2 2869
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 2868 . . 3  |-  ( A. y  e.  B  ( ph  /\  ps )  <->  ( A. y  e.  B  ph  /\  A. y  e.  B  ps ) )
21ralbii 2758 . 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 2868 . 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 249 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 setvar class
Syntax hints:    <-> wb 184    /\ wa 369   A.wral 2734
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-12 1792
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-ral 2739
This theorem is referenced by:  fununi  5503  tz7.48lem  6915  isffth2  14845  ispos2  15137  isnsg2  15730  efgred  16264  dfrhm2  16827  caucfil  20813  aalioulem6  21822  ajmoi  24278  adjmo  25255  iccllyscon  27158  dfso3  27395  ispridl2  28861  scmatsubcl  30907  scmatmulcl  30909  ishlat2  33021
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