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Theorem al2imi 1417
Description: Inference quantifying antecedent, nested antecedent, and consequent. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
al2imi.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
al2imi  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )

Proof of Theorem al2imi
StepHypRef Expression
1 al2imi.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21alimi 1414 . 2  |-  ( A. x ph  ->  A. x
( ps  ->  ch ) )
3 alim 1416 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( A. x ps  ->  A. x ch ) )
42, 3syl 14 1  |-  ( A. x ph  ->  ( A. x ps  ->  A. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1312
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-5 1406  ax-gen 1408
This theorem is referenced by:  alanimi  1418  alimdh  1426  albi  1427  19.30dc  1589  19.33b2  1591  hbnt  1614  ax10o  1676  spimth  1696  sbi1v  1845  ralim  2466  ceqsalt  2684  intss  3760
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