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Theorem con3dimp 625
Description: Variant of con3d 621 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 621 . 2  |-  ( ph  ->  ( -.  ch  ->  -. 
ps ) )
32imp 123 1  |-  ( (
ph  /\  -.  ch )  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> 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-in1 604  ax-in2 605
This theorem is referenced by:  nelneq  2241  nelneq2  2242  nelss  3162  nnnninf  7030  bcpasc  10543  fiinfnf1o  10563  pw1nct  13369
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