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Metamath Proof Explorer

Theorem e202

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

	Ref	Expression
Hypotheses	e202.1	$⊢ (φ, ψ \to χ)$
	e202.2	$⊢ θ$
	e202.3	$⊢ (φ, ψ \to τ)$
	e202.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	e202	$⊢ (φ, ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e202.1	$⊢ (φ, ψ \to χ)$
2		e202.2	$⊢ θ$
3		e202.3	$⊢ (φ, ψ \to τ)$
4		e202.4	$⊢ χ \to (θ \to (τ \to η))$
5	2	vd02	$⊢ (φ, ψ \to θ)$
6	1 5 3 4	e222	$⊢ (φ, ψ \to η)$