Theorem falnanfal 1583

Description: A ⊼ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

Ref	Expression
falnanfal	⊢ ((⊥ ⊼ ⊥) ↔ ⊤)

Proof of Theorem falnanfal

Step	Hyp	Ref	Expression
1		nannot 1494	. 2 ⊢ (¬ ⊥ ↔ (⊥ ⊼ ⊥))
2		notfal 1567	. 2 ⊢ (¬ ⊥ ↔ ⊤)
3	1, 2	bitr3i 276	1 ⊢ ((⊥ ⊼ ⊥) ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 205   ⊼ wnan 1486  ⊤wtru 1540  ⊥wfal 1551

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 206  df-an 397  df-nan 1487  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)