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Theorem imp42 594
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp42  |-  ( ( ( ph  /\  ( ps  /\  ch ) )  /\  th )  ->  ta )

Proof of Theorem imp42
StepHypRef Expression
1 imp4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21imp32 433 . 2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  -> 
( th  ->  ta ) )
32imp 429 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:  imp55  601  ltexprlem7  9421  iscatd  14931  isposd  15445  pospropd  15624  mulgghm2  18338  mulgghm2OLD  18341  ordtbaslem  19495  txbas  19895  grporcan  24996  chirredlem1  27082  cvxpcon  28438  cvxscon  28439  nocvxminlem  29303  rngonegmn1l  30182  prnc  30294
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