Metamath Proof Explorer


Theorem olcd

Description: Deduction introducing a disjunct. A translation of natural deduction rule \/ IL ( \/ insertion left), see natded . (Contributed by NM, 11-Apr-2008) (Proof shortened by Wolf Lammen, 3-Oct-2013)

Ref Expression
Hypothesis orcd.1
|- ( ph -> ps )
Assertion olcd
|- ( ph -> ( ch \/ ps ) )

Proof

Step Hyp Ref Expression
1 orcd.1
 |-  ( ph -> ps )
2 1 orcd
 |-  ( ph -> ( ps \/ ch ) )
3 2 orcomd
 |-  ( ph -> ( ch \/ ps ) )