Theorem pm5.21 831

Description: Two propositions are equivalent if they are both false. Theorem *5.21 of [WhiteheadRussell] p. 124. (Contributed by NM, 21-May-1994.)

Assertion

Ref	Expression
pm5.21	|- ((-. ph /\ -. ps) -> (ph <-> ps))

Proof of Theorem pm5.21

Step	Hyp	Ref	Expression
1		pm5.21im 338	. 2 |- (-. ph -> (-. ps -> (ph <-> ps)))
2	1	imp 418	1 |- ((-. ph /\ -. ps) -> (ph <-> ps))

This proof depends on syntax axioms:  -. wn 3   -> wi 4   <-> wb 176   /\ wa 358

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-an 360

This theorem is used by:  oibabs  851