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Theorem jcnd 642
Description: Deduction joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019.) (Proof shortened by Wolf Lammen, 10-Apr-2024.)
Hypotheses
Ref Expression
jcnd.1  |-  ( ph  ->  ps )
jcnd.2  |-  ( ph  ->  -.  ch )
Assertion
Ref Expression
jcnd  |-  ( ph  ->  -.  ( ps  ->  ch ) )

Proof of Theorem jcnd
StepHypRef Expression
1 jcnd.1 . 2  |-  ( ph  ->  ps )
2 jcnd.2 . 2  |-  ( ph  ->  -.  ch )
3 jcn 641 . 2  |-  ( ps 
->  ( -.  ch  ->  -.  ( ps  ->  ch ) ) )
41, 2, 3sylc 62 1  |-  ( ph  ->  -.  ( ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604  ax-in2 605
This theorem is referenced by: (None)
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