Description: XOR implies NAND (written with the -/\ connector). (Contributed by BJ, 19-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | xornan2 | ⊢ ( ( 𝜑 ⊻ 𝜓 ) → ( 𝜑 ⊼ 𝜓 ) ) |
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 ) ) |