Theorem falbifal 1575

Description: A ↔ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
falbifal	⊢ ((⊥ ↔ ⊥) ↔ ⊤)

Proof of Theorem falbifal

Step	Hyp	Ref	Expression
1		biid 264	. 2 ⊢ (⊥ ↔ ⊥)
2	1	bitru 1552	1 ⊢ ((⊥ ↔ ⊥) ↔ ⊤)

Syntax hints:   ↔ wb 209  ⊤wtru 1544  ⊥wfal 1555

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 210  df-tru 1546

This theorem is referenced by:  falxorfal  1591