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Theorem con3dimp 636
Description: Variant of con3d 632 with importation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.)
Hypothesis
Ref Expression
con3dimp.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
con3dimp  |-  ( (
ph  /\  -.  ch )  ->  -.  ps )

Proof of Theorem con3dimp
StepHypRef Expression
1 con3dimp.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21con3d 632 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
32imp 124 1  |-  ( (
ph  /\  -.  ch )  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 104
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-in1 615  ax-in2 616
This theorem is referenced by:  stoic1a  1438  nelneq  2290  nelneq2  2291  nelss  3231  nnnninf  7153  bcpasc  10777  fiinfnf1o  10797  nnoddn2prmb  12293  pcprod  12377  lgsdir  14889  pw1nct  15206
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