Theorem trubifal 1307

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 368	. 2 |- ( ( T. <-> F. ) <-> ( ( T. -> F. ) /\ ( F. -> T. ) ) )
2		truimfal 1301	. . 3 |- ( ( T. -> F. ) <-> F. )
3		falimtru 1302	. . 3 |- ( ( F. -> T. ) <-> T. )
4	2, 3	anbi12i 433	. 2 |- ( ( ( T. -> F. ) /\ ( F. -> T. ) ) <-> ( F. /\ T. ) )
5		falantru 1294	. 2 |- ( ( F. /\ T. ) <-> F. )
6	1, 4, 5	3bitri 195	1 |- ( ( T. <-> F. ) <-> F. )

Syntax hints:   -> wi 4   /\ wa 97   <-> wb 98   T. wtru 1244   F. wfal 1248

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249

This theorem is referenced by:  falbitru  1308