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Theorem 2alim 26907
Description: Theorem *11.32 in [WhiteheadRussell] p. 162. Theorem 19.20 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2alim  |-  ( A. x A. y ( ph  ->  ps )  ->  ( A. x A. y ph  ->  A. x A. y ps ) )

Proof of Theorem 2alim
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  ps )
)
212al2imi 26900 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 6   A.wal 1532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10  ax-5 1533  ax-gen 1536
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