Theorem syl6c 60

Description: Inference combining syl6 29 with contraction. (Contributed by Alan Sare, 2-May-2011.)

Hypotheses

Ref	Expression
syl6c.1	|- (ph -> (ps -> ch))
syl6c.2	|- (ph -> (ps -> th))
syl6c.3	|- (ch -> (th -> ta))

Assertion

Ref	Expression
syl6c	|- (ph -> (ps -> ta))

Proof of Theorem syl6c

Step	Hyp	Ref	Expression
1		syl6c.2	. 2 |- (ph -> (ps -> th))
2		syl6c.1	. . 3 |- (ph -> (ps -> ch))
3		syl6c.3	. . 3 |- (ch -> (th -> ta))
4	2, 3	syl6 29	. 2 |- (ph -> (ps -> (th -> ta)))
5	1, 4	mpdd 36	1 |- (ph -> (ps -> ta))

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7

This theorem is referenced by:  syldd  61  impbidd  181  pm5.21ndd  343  jcad  519  ee22  1362