Theorem trubifal 1600

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 225	. 2 ⊢ ((⊤ ↔ ⊥) ↔ (⊥ ↔ ⊤))
2		falbitru 1599	. 2 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)
3	1, 2	bitri 278	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:  truxorfal  1615  bj-vn0ALT  37736