ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  al2imi Unicode version

Theorem al2imi 1392
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 1389 . 2  |-  ( A. x ph  ->  A. x
( ps  ->  ch ) )
3 alim 1391 . 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 1287
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-5 1381  ax-gen 1383
This theorem is referenced by:  alanimi  1393  alimdh  1401  albi  1402  19.30dc  1563  19.33b2  1565  hbnt  1588  ax10o  1650  spimth  1670  sbi1v  1819  ralim  2434  ceqsalt  2645  intss  3709
  Copyright terms: Public domain W3C validator