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Theorem 2albi 27576
Description: Theorem *11.33 in [WhiteheadRussell] p. 162. Theorem 19.15 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2albi  |-  ( A. x A. y ( ph  <->  ps )  ->  ( A. x A. y ph  <->  A. x A. y ps ) )

Proof of Theorem 2albi
StepHypRef Expression
1 albi 1551 . . 3  |-  ( A. y ( ph  <->  ps )  ->  ( A. y ph  <->  A. y ps ) )
21alimi 1546 . 2  |-  ( A. x A. y ( ph  <->  ps )  ->  A. x
( A. y ph  <->  A. y ps ) )
3 albi 1551 . 2  |-  ( A. x ( A. y ph 
<-> 
A. y ps )  ->  ( A. x A. y ph  <->  A. x A. y ps ) )
42, 3syl 15 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:    -> wi 4    <-> wb 176   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177
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