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Theorem exp4d 609
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 )
)
21expd 436 . 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:  tfrlem9  7056  omass  7231  pssnn  7740  cardinfima  8481  ltexprlem7  9423  facdiv  12344  infpnlem1  14305  atcvatlem  27176  mdsymlem5  27198  mdsymlem7  27200  btwnconn1lem11  29722  exp5k  30096
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