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Metamath Proof Explorer

Theorem pm2.81

Description: Theorem *2.81 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.81 
|- ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) ) )

Proof

Step Hyp Ref Expression
1 orim2 
 |-  ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ph \/ ( ch -> th ) ) ) )
2 pm2.76 
 |-  ( ( ph \/ ( ch -> th ) ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) )
3 1 2 syl6 
 |-  ( ( ps -> ( ch -> th ) ) -> ( ( ph \/ ps ) -> ( ( ph \/ ch ) -> ( ph \/ th ) ) ) )