Theorem falbitru 1412

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

Assertion

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

Proof of Theorem falbitru

Step	Hyp	Ref	Expression
1		bicom 139	. 2 ⊢ ((⊥ ↔ ⊤) ↔ (⊤ ↔ ⊥))
2		trubifal 1411	. 2 ⊢ ((⊤ ↔ ⊥) ↔ ⊥)
3	1, 2	bitri 183	1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)

Syntax hints:   ↔ wb 104  ⊤wtru 1349  ⊥wfal 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by: (None)