Theorem trubifal 1411

Description: A <-> identity. (Contributed by David A. Wheeler, 23-Feb-2018.)

Assertion

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

Proof of Theorem trubifal

Step	Hyp	Ref	Expression
1		dfbi2 386	. 2 |- ( ( T. <-> F. ) <-> ( ( T. -> F. ) /\ ( F. -> T. ) ) )
2		truimfal 1405	. . 3 |- ( ( T. -> F. ) <-> F. )
3		falimtru 1406	. . 3 |- ( ( F. -> T. ) <-> T. )
4	2, 3	anbi12i 457	. 2 |- ( ( ( T. -> F. ) /\ ( F. -> T. ) ) <-> ( F. /\ T. ) )
5		falantru 1398	. 2 |- ( ( F. /\ T. ) <-> F. )
6	1, 4, 5	3bitri 205	1 |- ( ( T. <-> F. ) <-> F. )

Syntax hints:   -> wi 4   /\ wa 103   <-> 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:  falbitru  1412