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Theorem 2alimdv 1716
Description: Deduction form of Theorem 19.20 of [Margaris] p. 90 with two quantifiers, see alim 1637. (Contributed by NM, 27-Apr-2004.)
Hypothesis
Ref Expression
2alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
2alimdv  |-  ( ph  ->  ( A. x A. y ps  ->  A. x A. y ch ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)    ch( x, y)

Proof of Theorem 2alimdv
StepHypRef Expression
1 2alimdv.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21alimdv 1714 . 2  |-  ( ph  ->  ( A. y ps 
->  A. y ch )
)
32alimdv 1714 1  |-  ( ph  ->  ( A. x A. y ps  ->  A. x A. y ch ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1396
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-gen 1623  ax-4 1636  ax-5 1709
This theorem is referenced by:  soss  4807  dfwe2  6590  tz7.48lem  7098  ss2mcls  29195  mclsax  29196
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