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Theorem imp55 601
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
imp55  |-  ( ( ( ph  /\  ( ps  /\  ( ch  /\  th ) ) )  /\  ta )  ->  et )

Proof of Theorem imp55
StepHypRef Expression
1 imp5.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ( ta  ->  et )
) ) ) )
21imp4a 589 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ( ta  ->  et ) ) ) )
32imp42 594 1  |-  ( ( ( ph  /\  ( ps  /\  ( ch  /\  th ) ) )  /\  ta )  ->  et )
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 187  df-an 371
This theorem is referenced by:  alexsubALTlem4  20844
  Copyright terms: Public domain W3C validator