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Theorem imp32 253
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp3.1  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
Assertion
Ref Expression
imp32  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )

Proof of Theorem imp32
StepHypRef Expression
1 imp3.1 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
21impd 251 . 2  |-  ( ph  ->  ( ( ps  /\  ch )  ->  th )
)
32imp 122 1  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105
This theorem is referenced by:  imp42  346  impr  371  anasss  391  an13s  532  3expb  1140  reuss2  3251  reupick  3255  po2nr  4072  fvmptt  5294  fliftfund  5468  f1ocnv2d  5735  addclpi  6579  addnidpig  6588  mulnqprl  6820  mulnqpru  6821  ltsubrp  8849  ltaddrp  8850  divgcdcoprm0  10627
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