Metamath Proof Explorer

Theorem imbi2

Description: Theorem *4.85 of WhiteheadRussell p. 122. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 19-May-2013)

Ref Expression
Assertion imbi2 
|- ( ( ph <-> ps ) -> ( ( ch -> ph ) <-> ( ch -> ps ) ) )

Proof

Step Hyp Ref Expression
1 id 
 |-  ( ( ph <-> ps ) -> ( ph <-> ps ) )
2 1 imbi2d 
 |-  ( ( ph <-> ps ) -> ( ( ch -> ph ) <-> ( ch -> ps ) ) )