Theorem falbitru 1412

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

Assertion

Ref	Expression
falbitru	|- ( ( F. <-> T. ) <-> F. )

Proof of Theorem falbitru

Step	Hyp	Ref	Expression
1		bicom 139	. 2 |- ( ( F. <-> T. ) <-> ( T. <-> F. ) )
2		trubifal 1411	. 2 |- ( ( T. <-> F. ) <-> F. )
3	1, 2	bitri 183	1 |- ( ( F. <-> T. ) <-> F. )

Syntax hints:   <-> wb 104   T. wtru 1349   F. wfal 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354

This theorem is referenced by: (None)