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Theorem imp5a 581
Description: An importation inference. (Contributed by Jeff Hankins, 7-Jul-2009.)
Hypothesis
Ref Expression
imp5.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
Assertion
Ref Expression
imp5a  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ( th 
/\  ta )  ->  et ) ) ) )

Proof of Theorem imp5a
StepHypRef Expression
1 imp5.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
2 pm3.31 432 . 2  |-  ( ( th  ->  ( ta  ->  et ) )  -> 
( ( th  /\  ta )  ->  et ) )
31, 2syl8 65 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( ( th 
/\  ta )  ->  et ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  prtlem17  26744  tendospcanN  31213
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
  Copyright terms: Public domain W3C validator