Metamath Proof Explorer

Theorem trubifal

Description: A <-> identity. (Contributed by Anthony Hart, 22-Oct-2010) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 10-Jul-2020)

Ref Expression
Assertion trubifal ⊢ ⊤ ↔ ⊥ ↔ ⊥

Proof

Step Hyp Ref Expression
1 bicom ⊢ ⊤ ↔ ⊥ ↔ ⊥ ↔ ⊤
2 falbitru ⊢ ⊥ ↔ ⊤ ↔ ⊥
3 1 2 bitri ⊢ ⊤ ↔ ⊥ ↔ ⊥