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	$$⊢\phi$$
	mptxor.maj	$$⊢\left(\phi ⊻\psi \right)$$
Assertion	mptxor	$$⊢\neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		mptxor.min	$$⊢\phi$$
2		mptxor.maj	$$⊢\left(\phi ⊻\psi \right)$$
3		xornan	$$⊢\left(\phi ⊻\psi \right)\to \neg \left(\phi \wedge \psi \right)$$
4	2 3	ax-mp	$$⊢\neg \left(\phi \wedge \psi \right)$$
5	1 4	mptnan	$$⊢\neg \psi$$