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Theorem exp45 612
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 603 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32exp4a 604 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367
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 369
This theorem is referenced by:  oaass  7202  zorn2lem4  8870  zorn2lem7  8873  iscatd2  15170  fgss2  20541  alexsubALTlem4  20716  grporcan  25421  spansncvi  26768  mdsymlem5  27524  hbtlem2  31314  riotasv3d  35088  cvratlem  35542
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