Theorem syl6d

Description: A nested syllogism deduction. Deduction associated with syl6 . (Contributed by NM, 11-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl6d.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
	syl6d.2	|- ( ph -> ( th -> ta ) )
Assertion	syl6d	|- ( ph -> ( ps -> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl6d.1	|- ( ph -> ( ps -> ( ch -> th ) ) )
2		syl6d.2	|- ( ph -> ( th -> ta ) )
3	2	a1d	|- ( ph -> ( ps -> ( th -> ta ) ) )
4	1 3	syldd	|- ( ph -> ( ps -> ( ch -> ta ) ) )