Metamath Proof Explorer

Theorem imbi1

Description: Theorem *4.84 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion imbi1 
|- ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ( ph <-> ps ) -> ( ph <-> ps ) )
2 1 imbi1d 
 |-  ( ( ph <-> ps ) -> ( ( ph -> ch ) <-> ( ps -> ch ) ) )