Metamath Proof Explorer


Theorem pm5.21im

Description: Two propositions are equivalent if they are both false. Closed form of 2false . Equivalent to a biimpr -like version of the xor-connective. (Contributed by Wolf Lammen, 13-May-2013)

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

Proof

Step Hyp Ref Expression
1 nbn2
 |-  ( -. ph -> ( -. ps <-> ( ph <-> ps ) ) )
2 1 biimpd
 |-  ( -. ph -> ( -. ps -> ( ph <-> ps ) ) )