Theorem truimfal 1345

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

Assertion

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

Proof of Theorem truimfal

Step	Hyp	Ref	Expression
1		tru 1321	. . 3 |- T.
2	1	a1bi 327	. 2 |- ( F. <-> ( T. -> F. ))
3	2	bicomi 193	1 |- (( T. -> F. ) <-> F. )

This proof depends on syntax axioms:   -> wi 4   <-> wb 176   T. wtru 1316   F. wfal 1317

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 177  df-tru 1319

This theorem is used by: (None)