Description: Exclusive disjunction implies alternative denial ("XOR implies NAND"). (Contributed by BJ, 19-Apr-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | xornan | ⊢ ( ( 𝜑 ⊻ 𝜓 ) → ¬ ( 𝜑 ∧ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xor2 | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ( ( 𝜑 ∨ 𝜓 ) ∧ ¬ ( 𝜑 ∧ 𝜓 ) ) ) | |
2 | 1 | simprbi | ⊢ ( ( 𝜑 ⊻ 𝜓 ) → ¬ ( 𝜑 ∧ 𝜓 ) ) |