Theorem syl6ci 71

Description: A syllogism inference combined with contraction. (Contributed by Alan Sare, 18-Mar-2012.)

Hypotheses

Ref	Expression
syl6ci.1	|- ( ph -> ( ps -> ch ) )
syl6ci.2	|- ( ph -> th )
syl6ci.3	|- ( ch -> ( th -> ta ) )

Assertion

Ref	Expression
syl6ci	|- ( ph -> ( ps -> ta ) )

Proof of Theorem syl6ci

Step	Hyp	Ref	Expression
1		syl6ci.1	. 2 |- ( ph -> ( ps -> ch ) )
2		syl6ci.2	. . 3 |- ( ph -> th )
3	2	a1d 25	. 2 |- ( ph -> ( ps -> th ) )
4		syl6ci.3	. 2 |- ( ch -> ( th -> ta ) )
5	1, 3, 4	syl6c 70	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:  ordelord  5745  f1dmex  7136  omeulem2  7663  2pwuninel  8115  isumrpcl  14575  kqfvima  21533  caubl  23106  nbupgr  26240  nbumgrvtx  26242  umgr2adedgspth  26844  soseq  31751  btwnconn1lem12  32205  sbcim2g  38748  ee21an  38959