Metamath Proof Explorer

Theorem pm5.21

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

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

Proof

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