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Theorem imp4c 575
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 421 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  ( th 
->  ta ) ) )
32imp3a 421 1  |-  ( ph  ->  ( ( ( ps 
/\  ch )  /\  th )  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 359
This theorem is referenced by:  imp44  580  imp5g  584  riotasv3dOLD  6599  omordi  6809  omwordri  6815  omass  6823  oewordri  6835  elspansn5  23076  atcvat3i  23899  mdsymlem5  23910  sumdmdlem  23921  cvrat4  30240
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 178  df-an 361
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