Theorem 3syld

Description: Triple syllogism deduction. Deduction associated with 3syld . (Contributed by Jeff Hankins, 4-Aug-2009)

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

Proof

Step	Hyp	Ref	Expression
1		3syld.1	|- ( ph -> ( ps -> ch ) )
2		3syld.2	|- ( ph -> ( ch -> th ) )
3		3syld.3	|- ( ph -> ( th -> ta ) )
4	1 2	syld	|- ( ph -> ( ps -> th ) )
5	4 3	syld	|- ( ph -> ( ps -> ta ) )