Metamath Proof Explorer

Theorem pm5.42

Description: Theorem *5.42 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm5.42 
|- ( ( ph -> ( ps -> ch ) ) <-> ( ph -> ( ps -> ( ph /\ ch ) ) ) )

Proof

Step Hyp Ref Expression
1 ibar 
 |-  ( ph -> ( ch <-> ( ph /\ ch ) ) )
2 1 imbi2d 
 |-  ( ph -> ( ( ps -> ch ) <-> ( ps -> ( ph /\ ch ) ) ) )
3 2 pm5.74i 
 |-  ( ( ph -> ( ps -> ch ) ) <-> ( ph -> ( ps -> ( ph /\ ch ) ) ) )