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

Proof of Theorem trubifal

Step	Hyp	Ref	Expression
1		nottru 1348	. . 3 |- (-. T. <-> F. )
2		nbbn 347	. . 3 |- ((-. T. <-> F. ) <-> -. ( T. <-> F. ))
3	1, 2	mpbi 199	. 2 |- -. ( T. <-> F. )
4	3	bifal 1327	1 |- (( T. <-> F. ) <-> F. )

Syntax hints:  -. wn 3   <-> 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:  falbitru  1352  truxorfal  1359