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Metamath Proof Explorer

Theorem e23an

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e23an.1	$⊢ (φ, ψ \to χ)$
	e23an.2	$⊢ (φ, ψ, θ \to τ)$
	e23an.3	$⊢ (χ \land τ) \to η$
Assertion	e23an	$⊢ (φ, ψ, θ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e23an.1	$⊢ (φ, ψ \to χ)$
2		e23an.2	$⊢ (φ, ψ, θ \to τ)$
3		e23an.3	$⊢ (χ \land τ) \to η$
4	3	ex	$⊢ χ \to (τ \to η)$
5	1 2 4	e23	$⊢ (φ, ψ, θ \to η)$