Theorem falnantru 1597

Description: A ⊼ identity. (Contributed by Anthony Hart, 23-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

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

Proof of Theorem falnantru

Step	Hyp	Ref	Expression
1		nancom 1510	. 2 ⊢ ((⊥ ⊼ ⊤) ↔ (⊤ ⊼ ⊥))
2		trunanfal 1596	. 2 ⊢ ((⊤ ⊼ ⊥) ↔ ⊤)
3	1, 2	bitri 277	1 ⊢ ((⊥ ⊼ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 208   ⊼ wnan 1505  ⊤wtru 1555  ⊥wfal 1566

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 1506  df-tru 1557  df-fal 1567

This theorem is referenced by: (None)