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Theorem imp4c 574
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp4c  |-  ( ph  ->  ( ( ( ps 
/\  ch )  /\  th )  ->  ta ) )

Proof of Theorem imp4c
StepHypRef Expression
1 imp4.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21imp3a 420 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( th 
->  ta ) ) )
32imp3a 420 1  |-  ( ph  ->  ( ( ( ps 
/\  ch )  /\  th )  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  imp44  579  imp5g  583  riotasv3dOLD  6370  omordi  6580  omwordri  6586  omass  6594  oewordri  6606  elspansn5  22169  atcvat3i  22992  mdsymlem5  23003  sumdmdlem  23014  cvrat4  30254
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
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