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Metamath Proof Explorer

Theorem pm5.33

Description: Theorem *5.33 of WhiteheadRussell p. 125. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm5.33 
|- ( ( ph /\ ( ps -> ch ) ) <-> ( ph /\ ( ( ph /\ ps ) -> ch ) ) )

Proof

Step Hyp Ref Expression
1 ibar 
 |-  ( ph -> ( ps <-> ( ph /\ ps ) ) )
2 1 imbi1d 
 |-  ( ph -> ( ( ps -> ch ) <-> ( ( ph /\ ps ) -> ch ) ) )
3 2 pm5.32i 
 |-  ( ( ph /\ ( ps -> ch ) ) <-> ( ph /\ ( ( ph /\ ps ) -> ch ) ) )