Metamath Proof Explorer

Theorem imdi

Description: Distributive law for implication. Compare Theorem *5.41 of WhiteheadRussell p. 125. (Contributed by NM, 5-Aug-1993)

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

Proof

Step Hyp Ref Expression
1 ax-2 
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ps ) -> ( ph -> ch ) ) )
2 pm2.86 
 |-  ( ( ( ph -> ps ) -> ( ph -> ch ) ) -> ( ph -> ( ps -> ch ) ) )
3 1 2 impbii 
 |-  ( ( ph -> ( ps -> ch ) ) <-> ( ( ph -> ps ) -> ( ph -> ch ) ) )