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Theorem exp4d 592
Description: An exportation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
exp4d.1  |-  ( ph  ->  ( ( ps  /\  ( ch  /\  th )
)  ->  ta )
)
Assertion
Ref Expression
exp4d  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )

Proof of Theorem exp4d
StepHypRef Expression
1 exp4d.1 . . 3  |-  ( ph  ->  ( ( ps  /\  ( ch  /\  th )
)  ->  ta )
)
21exp3a 425 . 2  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
32exp4a 589 1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  tfrlem9  6417  omass  6594  pssnn  7097  cardinfima  7740  ltexprlem7  8682  facdiv  11316  infpnlem1  12973  atcvatlem  22981  mdsymlem5  23003  mdsymlem7  23005  btwnconn1lem11  24792  exp5k  26314
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