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Metamath Proof Explorer

Theorem ferison

Description: "Ferison", one of the syllogisms of Aristotelian logic. No ph is ps , and some ph is ch , therefore some ch is not ps . Instance of datisi . In Aristotelian notation, EIO-3: MeP and MiS therefore SoP. (Contributed by David A. Wheeler, 28-Aug-2016)

	Ref	Expression
Hypotheses	ferison.maj	\|- A. x ( ph -> -. ps )
	ferison.min	\|- E. x ( ph /\ ch )
Assertion	ferison	\|- E. x ( ch /\ -. ps )

Proof

Step	Hyp	Ref	Expression
1		ferison.maj	\|- A. x ( ph -> -. ps )
2		ferison.min	\|- E. x ( ph /\ ch )
3	1 2	datisi	\|- E. x ( ch /\ -. ps )