Theorem syl6c 66

Description: Inference combining syl6 33 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 33	. 2 |- ( ph -> ( ps -> ( th -> ta ) ) )
5	1, 4	mpdd 41	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  67  impbidd  126  jcad  305  dcbi  931  pm3.13dc  954  syl6ci  1438