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Metamath Proof Explorer

Theorem el021old

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	el021old.1	$⊢ φ$
	el021old.2	$⊢ ((ψ, χ) \to θ)$
	el021old.3	$⊢ (φ \land θ) \to τ$
Assertion	el021old	$⊢ ((ψ, χ) \to τ)$

Proof

Step	Hyp	Ref	Expression
1		el021old.1	$⊢ φ$
2		el021old.2	$⊢ ((ψ, χ) \to θ)$
3		el021old.3	$⊢ (φ \land θ) \to τ$
4	2	dfvd2ani	$⊢ (ψ \land χ) \to θ$
5	1 4 3	sylancr	$⊢ (ψ \land χ) \to τ$
6	5	dfvd2anir	$⊢ ((ψ, χ) \to τ)$