Theorem falantru 1414

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

Assertion

Ref	Expression
falantru	|- ( ( F. /\ T. ) <-> F. )

Proof of Theorem falantru

Step	Hyp	Ref	Expression
1		simpl 109	. 2 |- ( ( F. /\ T. ) -> F. )
2		falim 1378	. 2 |- ( F. -> ( F. /\ T. ) )
3	1, 2	impbii 126	1 |- ( ( F. /\ T. ) <-> F. )

Syntax hints:   /\ wa 104   <-> wb 105   T. wtru 1365   F. wfal 1369

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370

This theorem is referenced by:  trubifal  1427  falxortru  1432  falxorfal  1433