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Metamath Proof Explorer

Theorem e120

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 10-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e120.1	$⊢ (φ \to ψ)$
	e120.2	$⊢ (φ, χ \to θ)$
	e120.3	$⊢ τ$
	e120.4	$⊢ ψ \to (θ \to (τ \to η))$
Assertion	e120	$⊢ (φ, χ \to η)$

Proof

Step	Hyp	Ref	Expression
1		e120.1	$⊢ (φ \to ψ)$
2		e120.2	$⊢ (φ, χ \to θ)$
3		e120.3	$⊢ τ$
4		e120.4	$⊢ ψ \to (θ \to (τ \to η))$
5	1	vd12	$⊢ (φ, χ \to ψ)$
6	5 2 3 4	e220	$⊢ (φ, χ \to η)$