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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	$⊢ φ \to (ψ \lor χ)$
	olcnd.2	$⊢ φ \to \neg χ$
Assertion	olcnd	$⊢ φ \to ψ$

Proof

Step	Hyp	Ref	Expression
1		olcnd.1	$⊢ φ \to (ψ \lor χ)$
2		olcnd.2	$⊢ φ \to \neg χ$
3	1	ord	$⊢ φ \to (\neg ψ \to χ)$
4	2 3	mt3d	$⊢ φ \to ψ$