Theorem falantru 1334

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 107	. 2 |- ( ( F. /\ T. ) -> F. )
2		falim 1298	. 2 |- ( F. -> ( F. /\ T. ) )
3	1, 2	impbii 124	1 |- ( ( F. /\ T. ) <-> F. )

Syntax hints:   /\ 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:  trubifal  1347  falxortru  1352  falxorfal  1353