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Metamath Proof Explorer

Theorem pm2.61d

Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994) (Proof shortened by Wolf Lammen, 12-Sep-2013)

Ref Expression
Hypotheses pm2.61d.1 
|- ( ph -> ( ps -> ch ) )
pm2.61d.2 
|- ( ph -> ( -. ps -> ch ) )
Assertion pm2.61d 
|- ( ph -> ch )

Proof

Step Hyp Ref Expression
1 pm2.61d.1 
 |-  ( ph -> ( ps -> ch ) )
2 pm2.61d.2 
 |-  ( ph -> ( -. ps -> ch ) )
3 2 con1d 
 |-  ( ph -> ( -. ch -> ps ) )
4 3 1 syld 
 |-  ( ph -> ( -. ch -> ch ) )
5 4 pm2.18d 
 |-  ( ph -> ch )