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Theorem 3impd 1157
Description: Importation deduction for triple conjunction. (Contributed by NM, 26-Oct-2006.)
Hypothesis
Ref Expression
3imp1.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
3impd  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )

Proof of Theorem 3impd
StepHypRef Expression
1 3imp1.1 . . . 4  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
21com4l 83 . . 3  |-  ( ps 
->  ( ch  ->  ( th  ->  ( ph  ->  ta ) ) ) )
323imp 1137 . 2  |-  ( ( ps  /\  ch  /\  th )  ->  ( ph  ->  ta ) )
43com12 30 1  |-  ( ph  ->  ( ( ps  /\  ch  /\  th )  ->  ta ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ w3a 924
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem depends on definitions:  df-bi 115  df-3an 926
This theorem is referenced by:  3imp2  1158  3impexp  1371  oprabid  5681  iccid  9341
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