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Theorem imp5p 26220
Description: A triple importation inference. (Contributed by Jeff Hankins, 8-Jul-2009.)
Hypothesis
Ref Expression
3imp5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
imp5p  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th  /\  ta )  ->  et ) ) )

Proof of Theorem imp5p
StepHypRef Expression
1 3imp5.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21com52l 88 . . 3  |-  ( ch 
->  ( th  ->  ( ta  ->  ( ph  ->  ( ps  ->  et )
) ) ) )
323imp 1145 . 2  |-  ( ( ch  /\  th  /\  ta )  ->  ( ph  ->  ( ps  ->  et ) ) )
43com3l 75 1  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th  /\  ta )  ->  et ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936
  Copyright terms: Public domain W3C validator