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Theorem impel 30479
Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019.)
Hypotheses
Ref Expression
impel.1  |-  ( ph  ->  ( ps  ->  ch ) )
impel.2  |-  ( et 
->  ps )
Assertion
Ref Expression
impel  |-  ( (
ph  /\  et )  ->  ch )

Proof of Theorem impel
StepHypRef Expression
1 impel.2 . 2  |-  ( et 
->  ps )
2 impel.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
3 pm3.35 587 . 2  |-  ( ( ps  /\  ( ps 
->  ch ) )  ->  ch )
41, 2, 3syl2anr 478 1  |-  ( (
ph  /\  et )  ->  ch )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator