Theorem jc 640

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

Step	Hyp	Ref	Expression
1		jc.1	. 2 |- ( ph -> ps )
2		jc.2	. 2 |- ( ph -> ch )
3		pm3.2im 627	. 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 604  ax-in2 605

This theorem is referenced by: (None)