Theorem mptxor

Description: Modus ponendo tollens 2, one of the "indemonstrables" in Stoic logic. Note that this uses exclusive-or \/_ . See rule 2 on Lopez-Astorga p. 12 , rule 4 on Sanford p. 39 and rule A4 in Hitchcock p. 5 . (Contributed by David A. Wheeler, 3-Jul-2016) (Proof shortened by Wolf Lammen, 12-Nov-2017) (Proof shortened by BJ, 19-Apr-2019)

	Ref	Expression
Hypotheses	mptxor.min	|- ph
	mptxor.maj	|- ( ph \/_ ps )
Assertion	mptxor	|- -. ps

Proof

Step	Hyp	Ref	Expression
1		mptxor.min	|- ph
2		mptxor.maj	|- ( ph \/_ ps )
3		xornan	|- ( ( ph \/_ ps ) -> -. ( ph /\ ps ) )
4	2 3	ax-mp	|- -. ( ph /\ ps )
5	1 4	mptnan	|- -. ps