Theorem pm5.21 903

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 364	. 2 |- ( -. ph -> ( -. ps -> ( ph <-> ps ) ) )
2	1	imp 445	1 |- ( ( -. ph /\ -. ps ) -> ( ph <-> ps ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   /\ wa 384

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-an 386

This theorem is referenced by:  onsuct0  32440  wl-nfeqfb  33323  tsbi2  33941