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Metamath Proof Explorer

Theorem 3pm3.2ni

Description: Triple negated disjunction introduction. (Contributed by Scott Fenton, 20-Apr-2011)

Ref Expression
Hypotheses 3pm3.2ni.1 
|- -. ph
3pm3.2ni.2 
|- -. ps
3pm3.2ni.3 
|- -. ch
Assertion 3pm3.2ni 
|- -. ( ph \/ ps \/ ch )

Proof

Step Hyp Ref Expression
1 3pm3.2ni.1 
 |-  -. ph
2 3pm3.2ni.2 
 |-  -. ps
3 3pm3.2ni.3 
 |-  -. ch
4 1 2 pm3.2ni 
 |-  -. ( ph \/ ps )
5 4 3 pm3.2ni 
 |-  -. ( ( ph \/ ps ) \/ ch )
6 df-3or 
 |-  ( ( ph \/ ps \/ ch ) <-> ( ( ph \/ ps ) \/ ch ) )
7 5 6 mtbir 
 |-  -. ( ph \/ ps \/ ch )