Theorem falbitru 1570

Description: A ↔ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)

Assertion

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

Proof of Theorem falbitru

Step	Hyp	Ref	Expression
1		tbtru 1548	. 2 ⊢ (⊥ ↔ (⊥ ↔ ⊤))
2	1	bicomi 224	1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)

Syntax hints:   ↔ wb 206  ⊤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 207  df-tru 1543

This theorem is referenced by:  trubifal  1571