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Metamath Proof Explorer

Theorem syl5d

Description: A nested syllogism deduction. Deduction associated with syl5 . (Contributed by NM, 14-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000) (Proof shortened by Mel L. O'Cat, 2-Feb-2006)

	Ref	Expression
Hypotheses	syl5d.1	\|- ( ph -> ( ps -> ch ) )
	syl5d.2	\|- ( ph -> ( th -> ( ch -> ta ) ) )
Assertion	syl5d	\|- ( ph -> ( th -> ( ps -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		syl5d.1	\|- ( ph -> ( ps -> ch ) )
2		syl5d.2	\|- ( ph -> ( th -> ( ch -> ta ) ) )
3	1	a1d	\|- ( ph -> ( th -> ( ps -> ch ) ) )
4	3 2	syldd	\|- ( ph -> ( th -> ( ps -> ta ) ) )