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Theorem impel 274
Description: An inference for implication elimination. (Contributed by Giovanni Mascellani, 23-May-2019.) (Proof shortened by Wolf Lammen, 2-Sep-2020.)
Hypotheses
Ref Expression
impel.1  |-  ( ph  ->  ( ps  ->  ch ) )
impel.2  |-  ( th 
->  ps )
Assertion
Ref Expression
impel  |-  ( (
ph  /\  th )  ->  ch )

Proof of Theorem impel
StepHypRef Expression
1 impel.2 . . 3  |-  ( th 
->  ps )
2 impel.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2syl5 32 . 2  |-  ( ph  ->  ( th  ->  ch ) )
43imp 122 1  |-  ( (
ph  /\  th )  ->  ch )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem is referenced by:  eqinfti  6622  finomni  6701  frecuzrdgrclt  9711
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