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Theorem 19.26-2 1649
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 1648 . . 3  |-  ( A. y ( ph  /\  ps )  <->  ( A. y ph  /\  A. y ps ) )
21albii 1611 . 2  |-  ( A. x A. y ( ph  /\ 
ps )  <->  A. x
( A. y ph  /\ 
A. y ps )
)
3 19.26 1648 . 2  |-  ( A. x ( A. y ph  /\  A. y ps )  <->  ( A. x A. y ph  /\  A. x A. y ps )
)
42, 3bitri 249 1  |-  ( A. x A. y ( ph  /\ 
ps )  <->  ( A. x A. y ph  /\  A. x A. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  2mo2  2366  opelopabt  4702  fun11  5584  dford4  29519
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