Description: Two ways to write XNOR (exclusive not-or). (Contributed by Mario Carneiro, 4-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | xnor | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ↔ 𝜓 ) ) | |
2 | 1 | con2bii | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) |