Theorem falnanfal 1577

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 1488	. 2 ⊢ (¬ ⊥ ↔ (⊥ ⊼ ⊥))
2		notfal 1561	. 2 ⊢ (¬ ⊥ ↔ ⊤)
3	1, 2	bitr3i 279	1 ⊢ ((⊥ ⊼ ⊥) ↔ ⊤)

Syntax hints:  ¬ wn 3   ↔ wb 208   ⊼ wnan 1480  ⊤wtru 1534  ⊥wfal 1545

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 209  df-an 399  df-nan 1481  df-tru 1536  df-fal 1546

This theorem is referenced by: (None)