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Metamath Proof Explorer

Theorem syld

Description: Syllogism deduction. Deduction associated with syl . See conventions for the meaning of "associated deduction" or "deduction form". (Contributed by NM, 5-Aug-1993) (Proof shortened by Mel L. O'Cat, 19-Feb-2008) (Proof shortened by Wolf Lammen, 3-Aug-2012)

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

Proof

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