Theorem falbitru 1599

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 1577	. 2 ⊢ (⊥ ↔ (⊥ ↔ ⊤))
2	1	bicomi 227	1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)

This proof depends on syntax axioms:   ↔ wb 209  ⊤wtru 1570  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-tru 1572

This theorem is used by:  trubifal  1600