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Theorem imp4a 344
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
Assertion
Ref Expression
imp4a  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )

Proof of Theorem imp4a
StepHypRef Expression
1 imp4.1 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  ( th  ->  ta ) ) ) )
2 impexp 261 . 2  |-  ( ( ( ch  /\  th )  ->  ta )  <->  ( ch  ->  ( th  ->  ta ) ) )
31, 2syl6ibr 161 1  |-  ( ph  ->  ( ps  ->  (
( ch  /\  th )  ->  ta ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  imp4b  345  imp4d  347  imp55  356  imp511  357  equs5or  1784  reuss2  3324  tfrlem9  6182  facwordi  10426  ndvdssub  11523  neibl  12555
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