Theorem falbitru 1348

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 138	. 2 ⊢ ((⊥ ↔ ⊤) ↔ (⊤ ↔ ⊥))
2		trubifal 1347	. 2 ⊢ ((⊤ ↔ ⊥) ↔ ⊥)
3	1, 2	bitri 182	1 ⊢ ((⊥ ↔ ⊤) ↔ ⊥)

Syntax hints:   ↔ wb 103  ⊤wtru 1285  ⊥wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by: (None)