Theorem jcn 39205

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

Step	Hyp	Ref	Expression
1		jcn.1	. . 3 |- ( ph -> ps )
2		jcn.2	. . 3 |- ( ph -> -. ch )
3	1, 2	jc 159	. 2 |- ( ph -> -. ( ps -> -. -. ch ) )
4		notnotb 304	. . 3 |- ( ch <-> -. -. ch )
5	4	imbi2i 326	. 2 |- ( ( ps -> ch ) <-> ( ps -> -. -. ch ) )
6	3, 5	sylnibr 319	1 |- ( ph -> -. ( ps -> ch ) )

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 197

This theorem is referenced by:  limcrecl  39861