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Theorem 19.26-2 1593
Description: Theorem 19.26 of [Margaris] p. 90 with two quantifiers. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
19.26-2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x A. y ph  /\  A. x A. y ps ) )

Proof of Theorem 19.26-2
StepHypRef Expression
1 19.26 1592 . . 3  |-  ( A. y ( ph  /\  ps )  <->  ( A. y ph  /\  A. y ps ) )
21albii 1554 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  A. x
( A. y ph  /\ 
A. y ps )
)
3 19.26 1592 . 2  |-  ( A. x ( A. y ph  /\  A. y ps )  <->  ( A. x A. y ph  /\  A. x A. y ps )
)
42, 3bitri 242 1  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x A. y ph  /\  A. x A. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1532
This theorem is referenced by:  opelopabt  4214  fun11  5218  dford4  26454
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536
This theorem depends on definitions:  df-bi 179  df-an 362
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