Theorem xornan2

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

	Ref	Expression
Assertion	xornan2	⊢ ( ( 𝜑 ⊻ 𝜓 ) → ( 𝜑 ⊼ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		xornan	⊢ ( ( 𝜑 ⊻ 𝜓 ) → ¬ ( 𝜑 ∧ 𝜓 ) )
2		df-nan	⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )
3	1 2	sylibr	⊢ ( ( 𝜑 ⊻ 𝜓 ) → ( 𝜑 ⊼ 𝜓 ) )