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Theorem imp45 580
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp45  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  th ) ) )  ->  ta )

Proof of Theorem imp45
StepHypRef Expression
1 imp4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21imp4d 575 . 2  |-  ( ph  ->  ( ( ps  /\  ( ch  /\  th )
)  ->  ta )
)
32imp 418 1  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  th ) ) )  ->  ta )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  alexsubALTlem3  17743  spansncvi  22231  atcvatlem  22965
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
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