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Theorem 19.33-2 27580
Description: Theorem *11.421 in [WhiteheadRussell] p. 163. Theorem 19.33 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.33-2  |-  ( ( A. x A. y ph  \/  A. x A. y ps )  ->  A. x A. y ( ph  \/  ps ) )

Proof of Theorem 19.33-2
StepHypRef Expression
1 orc 374 . . 3  |-  ( ph  ->  ( ph  \/  ps ) )
212alimi 1547 . 2  |-  ( A. x A. y ph  ->  A. x A. y (
ph  \/  ps )
)
3 olc 373 . . 3  |-  ( ps 
->  ( ph  \/  ps ) )
432alimi 1547 . 2  |-  ( A. x A. y ps  ->  A. x A. y (
ph  \/  ps )
)
52, 4jaoi 368 1  |-  ( ( A. x A. y ph  \/  A. x A. y ps )  ->  A. x A. y ( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    \/ wo 357   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  df-or 359
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