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Theorem alimdv 1807
Description: Deduction from Theorem 19.20 of [Margaris] p. 90. (Contributed by NM, 3-Apr-1994.)
Hypothesis
Ref Expression
alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
alimdv  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem alimdv
StepHypRef Expression
1 ax-17 1464 . 2  |-  ( ph  ->  A. x ph )
2 alimdv.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alimdh 1401 1  |-  ( ph  ->  ( A. x ps 
->  A. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-gen 1383  ax-17 1464
This theorem is referenced by:  2alimdv  1809  moim  2012  ralimdv2  2443  sstr2  3032  reuss2  3279  ssuni  3675  disjss2  3825  disjss1  3828  disjiun  3840  soss  4141  alxfr  4283  ssrel  4526  ssrel2  4528  ssrelrel  4538  iotaval  4991
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