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Theorem jc 139
Description: Inference joining the consequents of two premises. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
jc.1  |-  ( ph  ->  ps )
jc.2  |-  ( ph  ->  ch )
Assertion
Ref Expression
jc  |-  ( ph  ->  -.  ( ps  ->  -. 
ch ) )

Proof of Theorem jc
StepHypRef Expression
1 jc.1 . 2  |-  ( ph  ->  ps )
2 jc.2 . 2  |-  ( ph  ->  ch )
3 pm3.2im 137 . 2  |-  ( ps 
->  ( ch  ->  -.  ( ps  ->  -.  ch ) ) )
41, 2, 3sylc 56 1  |-  ( ph  ->  -.  ( ps  ->  -. 
ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  isprm5  12791
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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