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Metamath Proof Explorer

Theorem pm2.65

Description: Theorem *2.65 of WhiteheadRussell p. 107. Proof by contradiction. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 8-Mar-2013)

Ref Expression
Assertion pm2.65 
|- ( ( ph -> ps ) -> ( ( ph -> -. ps ) -> -. ph ) )

Proof

Step Hyp Ref Expression
1 idd 
 |-  ( ( ph -> ps ) -> ( -. ph -> -. ph ) )
2 con3 
 |-  ( ( ph -> ps ) -> ( -. ps -> -. ph ) )
3 1 2 jad 
 |-  ( ( ph -> ps ) -> ( ( ph -> -. ps ) -> -. ph ) )