Metamath Proof Explorer

Theorem falxortru

Description: A \/_ identity. (Contributed by David A. Wheeler, 9-May-2015) (Proof shortened by Wolf Lammen, 10-Jul-2020)

Ref Expression
Assertion falxortru ⊢ ⊥ ⊻ ⊤ ↔ ⊤

Proof

Step Hyp Ref Expression
1 xorcom ⊢ ⊥ ⊻ ⊤ ↔ ⊤ ⊻ ⊥
2 truxorfal ⊢ ⊤ ⊻ ⊥ ↔ ⊤
3 1 2 bitri ⊢ ⊥ ⊻ ⊤ ↔ ⊤