Theorem trubifal 1347

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 380	. 2 |- ( ( T. <-> F. ) <-> ( ( T. -> F. ) /\ ( F. -> T. ) ) )
2		truimfal 1341	. . 3 |- ( ( T. -> F. ) <-> F. )
3		falimtru 1342	. . 3 |- ( ( F. -> T. ) <-> T. )
4	2, 3	anbi12i 447	. 2 |- ( ( ( T. -> F. ) /\ ( F. -> T. ) ) <-> ( F. /\ T. ) )
5		falantru 1334	. 2 |- ( ( F. /\ T. ) <-> F. )
6	1, 4, 5	3bitri 204	1 |- ( ( T. <-> F. ) <-> F. )

Syntax hints:   -> wi 4   /\ wa 102   <-> wb 103   T. wtru 1285   F. wfal 1289

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 576  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-fal 1290

This theorem is referenced by:  falbitru  1348