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Metamath Proof Explorer

Theorem orcd

Description: Deduction introducing a disjunct. A translation of natural deduction rule \/ IR ( \/ insertion right), see natded . (Contributed by NM, 20-Sep-2007)

		Ref	Expression
	Hypothesis	orcd.1	$⊢ φ \to ψ$
	Assertion	orcd	$⊢ φ \to (ψ \lor χ)$

Proof

Step	Hyp	Ref	Expression
1		orcd.1	$⊢ φ \to ψ$
2		orc	$⊢ ψ \to (ψ \lor χ)$
3	1 2	syl	$⊢ φ \to (ψ \lor χ)$