Theorem falnanfal 1357

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 1293	. 2 ⊢ (¬ ⊥ ↔ ( ⊥ ⊼ ⊥ ))
2		notfal 1349	. 2 ⊢ (¬ ⊥ ↔ ⊤ )
3	1, 2	bitr3i 242	1 ⊢ (( ⊥ ⊼ ⊥ ) ↔ ⊤ )

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊼ wnan 1287   ⊤ wtru 1316   ⊥ wfal 1317

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 177  df-an 360  df-nan 1288  df-tru 1319  df-fal 1320

This theorem is referenced by: (None)