Theorem falbifal 1572

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 260	. 2 ⊢ (⊥ ↔ ⊥)
2	1	bitru 1549	1 ⊢ ((⊥ ↔ ⊥) ↔ ⊤)

Syntax hints:   ↔ wb 205  ⊤wtru 1541  ⊥wfal 1552

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 206  df-tru 1543

This theorem is referenced by:  falxorfal  1588