Theorem trubifal 1522

Description: A <-> identity. (Contributed by Anthony Hart, 22-Oct-2010.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 10-Jul-2020.)

Assertion

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

Proof of Theorem trubifal

Step	Hyp	Ref	Expression
1		bicom 212	. 2 |- ( ( T. <-> F. ) <-> ( F. <-> T. ) )
2		falbitru 1521	. 2 |- ( ( F. <-> T. ) <-> F. )
3	1, 2	bitri 264	1 |- ( ( T. <-> F. ) <-> F. )

Syntax hints:   <-> wb 196   T. wtru 1484   F. wfal 1488

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 197  df-tru 1486

This theorem is referenced by:  truxorfal  1529