Theorem jc 139

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 137	. 2 |- (ps -> (ch -> -. (ps -> -. ch)))
4	1, 2, 3	sylc 56	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: (None)