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Metamath Proof Explorer

Theorem pm2.61iii

Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002) (Proof shortened by Wolf Lammen, 22-Sep-2013)

Ref Expression
Hypotheses pm2.61iii.1 
|- ( -. ph -> ( -. ps -> ( -. ch -> th ) ) )
pm2.61iii.2 
|- ( ph -> th )
pm2.61iii.3 
|- ( ps -> th )
pm2.61iii.4 
|- ( ch -> th )
Assertion pm2.61iii 
|- th

Proof

Step Hyp Ref Expression
1 pm2.61iii.1 
 |-  ( -. ph -> ( -. ps -> ( -. ch -> th ) ) )
2 pm2.61iii.2 
 |-  ( ph -> th )
3 pm2.61iii.3 
 |-  ( ps -> th )
4 pm2.61iii.4 
 |-  ( ch -> th )
5 2 a1d 
 |-  ( ph -> ( -. ch -> th ) )
6 3 a1d 
 |-  ( ps -> ( -. ch -> th ) )
7 1 5 6 pm2.61ii 
 |-  ( -. ch -> th )
8 4 7 pm2.61i 
 |-  th