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Theorem exp45 614
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp45.1  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  th ) ) )  ->  ta )
Assertion
Ref Expression
exp45  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp45
StepHypRef Expression
1 exp45.1 . . 3  |-  ( (
ph  /\  ( ps  /\  ( ch  /\  th ) ) )  ->  ta )
21exp32 605 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32exp4a 606 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
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 185  df-an 371
This theorem is referenced by:  oaass  7103  zorn2lem4  8772  zorn2lem7  8775  iscatd2  14730  fgss2  19572  alexsubALTlem4  19747  grporcan  23853  spansncvi  25200  mdsymlem5  25956  hbtlem2  29621  riotasv3d  32920  cvratlem  33374
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