Theorem jcnd 653

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

Step	Hyp	Ref	Expression
1		jcnd.1	. 2 |- ( ph -> ps )
2		jcnd.2	. 2 |- ( ph -> -. ch )
3		jcn 652	. 2 |- ( ps -> ( -. ch -> -. ( ps -> ch ) ) )
4	1, 2, 3	sylc 62	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-in1 615  ax-in2 616

This theorem is referenced by: (None)