Description: The connector \/_ is negated under negation of one argument. (Contributed by Mario Carneiro, 4-Sep-2016) (Proof shortened by Wolf Lammen, 27-Jun-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | xorneg2 | ⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xor | ⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ↔ ¬ 𝜓 ) ) | |
2 | pm5.18 | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ↔ ¬ 𝜓 ) ) | |
3 | xnor | ⊢ ( ( 𝜑 ↔ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) | |
4 | 1 2 3 | 3bitr2i | ⊢ ( ( 𝜑 ⊻ ¬ 𝜓 ) ↔ ¬ ( 𝜑 ⊻ 𝜓 ) ) |