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Metamath Proof Explorer

Theorem pm2.82

Description: Theorem *2.82 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.82 
|- ( ( ( ph \/ ps ) \/ ch ) -> ( ( ( ph \/ -. ch ) \/ th ) -> ( ( ph \/ ps ) \/ th ) ) )

Proof

Step Hyp Ref Expression
1 pm2.24 
 |-  ( ch -> ( -. ch -> ps ) )
2 1 orim2d 
 |-  ( ch -> ( ( ph \/ -. ch ) -> ( ph \/ ps ) ) )
3 2 jao1i 
 |-  ( ( ( ph \/ ps ) \/ ch ) -> ( ( ph \/ -. ch ) -> ( ph \/ ps ) ) )
4 3 orim1d 
 |-  ( ( ( ph \/ ps ) \/ ch ) -> ( ( ( ph \/ -. ch ) \/ th ) -> ( ( ph \/ ps ) \/ th ) ) )