Theorem trubifal 1571

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
trubifal	⊢ ((⊤ ↔ ⊥) ↔ ⊥)

Proof of Theorem trubifal

Step	Hyp	Ref	Expression
1		bicom 222	. 2 ⊢ ((⊤ ↔ ⊥) ↔ (⊥ ↔ ⊤))
2		falbitru 1570	. 2 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)
3	1, 2	bitri 275	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:  truxorfal  1586