Description: A -\/ identity. (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 17-Dec-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | trunorfal | ⊢ ( ( ⊤ ⊽ ⊥ ) ↔ ⊥ ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-nor | ⊢ ( ( ⊤ ⊽ ⊥ ) ↔ ¬ ( ⊤ ∨ ⊥ ) ) | |
2 | truorfal | ⊢ ( ( ⊤ ∨ ⊥ ) ↔ ⊤ ) | |
3 | 1 2 | xchbinx | ⊢ ( ( ⊤ ⊽ ⊥ ) ↔ ¬ ⊤ ) |
4 | df-fal | ⊢ ( ⊥ ↔ ¬ ⊤ ) | |
5 | 3 4 | bitr4i | ⊢ ( ( ⊤ ⊽ ⊥ ) ↔ ⊥ ) |