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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	⊢ ( 𝜑 → 𝜓 )
	Assertion	olcd	⊢ ( 𝜑 → ( 𝜒 ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		orcd.1	⊢ ( 𝜑 → 𝜓 )
2	1	orcd	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
3	2	orcomd	⊢ ( 𝜑 → ( 𝜒 ∨ 𝜓 ) )