Metamath Proof Explorer


Theorem xornan2

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

Ref Expression
Assertion xornan2 ( ( 𝜑𝜓 ) → ( 𝜑𝜓 ) )

Proof

Step Hyp Ref Expression
1 xornan ( ( 𝜑𝜓 ) → ¬ ( 𝜑𝜓 ) )
2 df-nan ( ( 𝜑𝜓 ) ↔ ¬ ( 𝜑𝜓 ) )
3 1 2 sylibr ( ( 𝜑𝜓 ) → ( 𝜑𝜓 ) )