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Theorem al2imi 1388
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 1385 . 2  |-  ( A. x ph  ->  A. x
( ps  ->  ch ) )
3 alim 1387 . 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 1283
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1377  ax-gen 1379
This theorem is referenced by:  alanimi  1389  alimdh  1397  albi  1398  19.30dc  1559  19.33b2  1561  hbnt  1584  ax10o  1644  spimth  1664  sbi1v  1813  ralim  2423  ceqsalt  2626  intss  3665
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