Theorem orcnd

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017)

	Ref	Expression
Hypotheses	orcnd.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
	orcnd.2	⊢ ( 𝜑 → ¬ 𝜓 )
Assertion	orcnd	⊢ ( 𝜑 → 𝜒 )

Proof

Step	Hyp	Ref	Expression
1		orcnd.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
2		orcnd.2	⊢ ( 𝜑 → ¬ 𝜓 )
3	1	orcomd	⊢ ( 𝜑 → ( 𝜒 ∨ 𝜓 ) )
4	3 2	olcnd	⊢ ( 𝜑 → 𝜒 )