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Metamath Proof Explorer

Theorem con2i

Description: A contraposition inference. Its associated inference is mt2 . (Contributed by NM, 10-Jan-1993) (Proof shortened by Mel L. O'Cat, 28-Nov-2008) (Proof shortened by Wolf Lammen, 13-Jun-2013)

		Ref	Expression
	Hypothesis	con2i.a	\|- ( ph -> -. ps )
	Assertion	con2i	\|- ( ps -> -. ph )

Proof

Step	Hyp	Ref	Expression
1		con2i.a	\|- ( ph -> -. ps )
2		id	\|- ( ps -> ps )
3	1 2	nsyl3	\|- ( ps -> -. ph )