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Theorem 2alimdv 2019
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (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 2017 . 2  |-  ( ph  ->  ( A. y ps 
->  A. y ch )
)
32alimdv 2017 1  |-  ( ph  ->  ( A. x A. y ps  ->  A. x A. y ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532
This theorem is referenced by:  soss  4225  dfwe2  4464  tz7.48lem  6339
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-nf 1540
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