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Metamath Proof Explorer

Theorem olcnd

Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017) (Proof shortened by Wolf Lammen, 13-Apr-2024)

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

Proof

Step	Hyp	Ref	Expression
1		olcnd.1	⊢ ( 𝜑 → ( 𝜓 ∨ 𝜒 ) )
2		olcnd.2	⊢ ( 𝜑 → ¬ 𝜒 )
3	1	ord	⊢ ( 𝜑 → ( ¬ 𝜓 → 𝜒 ) )
4	2 3	mt3d	⊢ ( 𝜑 → 𝜓 )