Theorem syl56 34

Description: Combine syl5 32 and syl6 33. (Contributed by NM, 14-Nov-2013.)

Hypotheses

Ref	Expression
syl56.1	|- ( ph -> ps )
syl56.2	|- ( ch -> ( ps -> th ) )
syl56.3	|- ( th -> ta )

Assertion

Ref	Expression
syl56	|- ( ch -> ( ph -> ta ) )

Proof of Theorem syl56

Step	Hyp	Ref	Expression
1		syl56.1	. 2 |- ( ph -> ps )
2		syl56.2	. . 3 |- ( ch -> ( ps -> th ) )
3		syl56.3	. . 3 |- ( th -> ta )
4	2, 3	syl6 33	. 2 |- ( ch -> ( ps -> ta ) )
5	1, 4	syl5 32	1 |- ( ch -> ( ph -> 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:  cbv2h  1746  cbv2w  1748  euind  2922  reuind  2940  sbcimdv  3026  cores  5124  prnmaxl  7462  prnminu  7463  pc2dvds  12296