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Theorem jcn 37431
Description: Inference joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019.)
Hypotheses
Ref Expression
jcn.1  |-  ( ph  ->  ps )
jcn.2  |-  ( ph  ->  -.  ch )
Assertion
Ref Expression
jcn  |-  ( ph  ->  -.  ( ps  ->  ch ) )

Proof of Theorem jcn
StepHypRef Expression
1 jcn.1 . . 3  |-  ( ph  ->  ps )
2 jcn.2 . . 3  |-  ( ph  ->  -.  ch )
31, 2jc 152 . 2  |-  ( ph  ->  -.  ( ps  ->  -. 
-.  ch ) )
4 notnot 297 . . 3  |-  ( ch  <->  -. 
-.  ch )
54imbi2i 319 . 2  |-  ( ( ps  ->  ch )  <->  ( ps  ->  -.  -.  ch ) )
63, 5sylnibr 312 1  |-  ( ph  ->  -.  ( ps  ->  ch ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 190
This theorem is referenced by:  limcrecl  37806
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