Theorem falbitru 1352

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

Assertion

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

Proof of Theorem falbitru

Step	Hyp	Ref	Expression
1		bicom 191	. 2 ⊢ (( ⊥ ↔ ⊤ ) ↔ ( ⊤ ↔ ⊥ ))
2		trubifal 1351	. 2 ⊢ (( ⊤ ↔ ⊥ ) ↔ ⊥ )
3	1, 2	bitri 240	1 ⊢ (( ⊥ ↔ ⊤ ) ↔ ⊥ )

Syntax hints:   ↔ 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:  falxortru  1360