Metamath Proof Explorer


Theorem trunorfal

Description: A -\/ identity. (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 17-Dec-2023)

Ref Expression
Assertion trunorfal ( ( ⊤ ⊥ ) ↔ ⊥ )

Proof

Step Hyp Ref Expression
1 df-nor ( ( ⊤ ⊥ ) ↔ ¬ ( ⊤ ∨ ⊥ ) )
2 truorfal ( ( ⊤ ∨ ⊥ ) ↔ ⊤ )
3 1 2 xchbinx ( ( ⊤ ⊥ ) ↔ ¬ ⊤ )
4 df-fal ( ⊥ ↔ ¬ ⊤ )
5 3 4 bitr4i ( ( ⊤ ⊥ ) ↔ ⊥ )