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	|- (( F. <-> T. ) <-> F. )

Proof of Theorem falbitru

Step	Hyp	Ref	Expression
1		bicom 191	. 2 |- (( F. <-> T. ) <-> ( T. <-> F. ))
2		trubifal 1351	. 2 |- (( T. <-> F. ) <-> F. )
3	1, 2	bitri 240	1 |- (( F. <-> T. ) <-> F. )

Syntax hints:   <-> wb 176   T. wtru 1316   F. 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