Theorem trunantru 1549

Description: A ⊼ identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.)

Assertion

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

Proof of Theorem trunantru

Step	Hyp	Ref	Expression
1		nannot 1474	. 2 ⊢ (¬ ⊤ ↔ (⊤ ⊼ ⊤))
2		nottru 1535	. 2 ⊢ (¬ ⊤ ↔ ⊥)
3	1, 2	bitr3i 269	1 ⊢ ((⊤ ⊼ ⊤) ↔ ⊥)

Syntax hints:  ¬ wn 3   ↔ wb 198   ⊼ wnan 1464  ⊤wtru 1509  ⊥wfal 1520

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 199  df-an 388  df-nan 1465  df-fal 1521

This theorem is referenced by: (None)