Theorem xornan2

Description: XOR implies NAND (written with the -/\ connector). (Contributed by BJ, 19-Apr-2019)

	Ref	Expression
Assertion	xornan2	$$⊢\left(\phi ⊻\psi \right)\to \left(\phi ⊼\psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		xornan	$$⊢\left(\phi ⊻\psi \right)\to \neg \left(\phi \wedge \psi \right)$$
2		df-nan	$$⊢\left(\phi ⊼\psi \right)\leftrightarrow \neg \left(\phi \wedge \psi \right)$$
3	1 2	sylibr	$$⊢\left(\phi ⊻\psi \right)\to \left(\phi ⊼\psi \right)$$