Theorem truorfal 1417

Description: A ∨ identity. (Contributed by Anthony Hart, 22-Oct-2010.)

Assertion

Ref	Expression
truorfal	⊢ ((⊤ ∨ ⊥) ↔ ⊤)

Proof of Theorem truorfal

Step	Hyp	Ref	Expression
1		tru 1368	. . 3 ⊢ ⊤
2	1	orci 732	. 2 ⊢ (⊤ ∨ ⊥)
3	2	bitru 1376	1 ⊢ ((⊤ ∨ ⊥) ↔ ⊤)

Syntax hints:   ↔ wb 105   ∨ wo 709  ⊤wtru 1365  ⊥wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117  df-tru 1367

This theorem is referenced by:  truxorfal  1431