Description: The connector \/_ is unchanged under negation of both arguments. (Contributed by Mario Carneiro, 4-Sep-2016)
Ref | Expression | ||
---|---|---|---|
Assertion | xorneg | ⊢ ( ( ¬ 𝜑 ⊻ ¬ 𝜓 ) ↔ ( 𝜑 ⊻ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xorneg1 | ⊢ ( ( ¬ 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ ¬ 𝜓 ) ) | |
2 | xorneg2 | ⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) | |
3 | 2 | con2bii | ⊢ ( ( 𝜑 ⊻ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ ¬ 𝜓 ) ) |
4 | 1 3 | bitr4i | ⊢ ( ( ¬ 𝜑 ⊻ ¬ 𝜓 ) ↔ ( 𝜑 ⊻ 𝜓 ) ) |