Theorem falantru 1340

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 108	. 2 |- ( ( F. /\ T. ) -> F. )
2		falim 1304	. 2 |- ( F. -> ( F. /\ T. ) )
3	1, 2	impbii 125	1 |- ( ( F. /\ T. ) <-> F. )

Syntax hints:   /\ wa 103   <-> wb 104   T. wtru 1291   F. wfal 1295

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-fal 1296

This theorem is referenced by:  trubifal  1353  falxortru  1358  falxorfal  1359