Theorem xornan

Description: Exclusive disjunction implies alternative denial ("XOR implies NAND"). (Contributed by BJ, 19-Apr-2019)

	Ref	Expression
Assertion	xornan	$$⊢\left(\phi ⊻\psi \right)\to \neg \left(\phi \wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		xor2	$$⊢\left(\phi ⊻\psi \right)\leftrightarrow \left(\left(\phi \vee \psi \right)\wedge \neg \left(\phi \wedge \psi \right)\right)$$
2	1	simprbi	$$⊢\left(\phi ⊻\psi \right)\to \neg \left(\phi \wedge \psi \right)$$