Theorem falnantru 1582

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 1488	. 2 ⊢ ((⊥ ⊼ ⊤) ↔ (⊤ ⊼ ⊥))
2		trunanfal 1581	. 2 ⊢ ((⊤ ⊼ ⊥) ↔ ⊤)
3	1, 2	bitri 274	1 ⊢ ((⊥ ⊼ ⊤) ↔ ⊤)

Syntax hints:   ↔ wb 205   ⊼ wnan 1483  ⊤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 396  df-nan 1484  df-tru 1542  df-fal 1552

This theorem is referenced by: (None)