Theorem falnantru 1612

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 1525	. 2 ⊢ ((⊥ ⊼ ⊤) ↔ (⊤ ⊼ ⊥))
2		trunanfal 1611	. 2 ⊢ ((⊤ ⊼ ⊥) ↔ ⊤)
3	1, 2	bitri 278	1 ⊢ ((⊥ ⊼ ⊤) ↔ ⊤)

This proof depends on syntax axioms:   ↔ wb 209   ⊼ wnan 1520  ⊤wtru 1570  ⊥wfal 1581

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 401  df-nan 1521  df-tru 1572  df-fal 1582

This theorem is used by: (None)