Metamath Proof Explorer

Theorem pm5.1

Description: Two propositions are equivalent if they are both true. Theorem *5.1 of WhiteheadRussell p. 123. (Contributed by NM, 21-May-1994)

Ref Expression
Assertion pm5.1 
|- ( ( ph /\ ps ) -> ( ph <-> ps ) )

Proof

Step Hyp Ref Expression
1 pm5.501 
 |-  ( ph -> ( ps <-> ( ph <-> ps ) ) )
2 1 biimpa 
 |-  ( ( ph /\ ps ) -> ( ph <-> ps ) )