Theorem trubifal 1351

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

Assertion

Ref	Expression
trubifal	⊢ (( ⊤ ↔ ⊥ ) ↔ ⊥ )

Proof of Theorem trubifal

Step	Hyp	Ref	Expression
1		nottru 1348	. . 3 ⊢ (¬ ⊤ ↔ ⊥ )
2		nbbn 347	. . 3 ⊢ ((¬ ⊤ ↔ ⊥ ) ↔ ¬ ( ⊤ ↔ ⊥ ))
3	1, 2	mpbi 199	. 2 ⊢ ¬ ( ⊤ ↔ ⊥ )
4	3	bifal 1327	1 ⊢ (( ⊤ ↔ ⊥ ) ↔ ⊥ )

Syntax hints:  ¬ wn 3   ↔ wb 176   ⊤ 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-tru 1319  df-fal 1320

This theorem is referenced by:  falbitru  1352  truxorfal  1359