Metamath Proof Explorer

Theorem pm2.83

Description: Theorem *2.83 of WhiteheadRussell p. 108. Closed form of syld . (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.83 
|- ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ( ch -> th ) ) -> ( ph -> ( ps -> th ) ) ) )

Proof

Step Hyp Ref Expression
1 imim1 
 |-  ( ( ps -> ch ) -> ( ( ch -> th ) -> ( ps -> th ) ) )
2 1 imim3i 
 |-  ( ( ph -> ( ps -> ch ) ) -> ( ( ph -> ( ch -> th ) ) -> ( ph -> ( ps -> th ) ) ) )