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Metamath Proof Explorer

Theorem pm2.18da

Description: Deduction based on reductio ad absurdum. See pm2.18 . (Contributed by Mario Carneiro, 9-Feb-2017)

Ref Expression
Hypothesis pm2.18da.1 
|- ( ( ph /\ -. ps ) -> ps )
Assertion pm2.18da 
|- ( ph -> ps )

Proof

Step Hyp Ref Expression
1 pm2.18da.1 
 |-  ( ( ph /\ -. ps ) -> ps )
2 1 ex 
 |-  ( ph -> ( -. ps -> ps ) )
3 2 pm2.18d 
 |-  ( ph -> ps )