Theorem jc 159

Description: Deduction joining the consequents of two premises. A deduction associated with pm3.2im 157. (Contributed by NM, 28-Dec-1992.)

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 157	. 2 |- ( ps -> ( ch -> -. ( ps -> -. ch ) ) )
4	1, 2, 3	sylc 65	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 is referenced by:  isprm5  15419  jcn  39205