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Metamath Proof Explorer

Theorem e20

Description: A virtual deduction elimination rule (see syl6mpi ). (Contributed by Alan Sare, 14-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e20.1	$⊢ (φ, ψ \to χ)$
	e20.2	$⊢ θ$
	e20.3	$⊢ χ \to (θ \to τ)$
Assertion	e20	$⊢ (φ, ψ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		e20.1	$⊢ (φ, ψ \to χ)$
2		e20.2	$⊢ θ$
3		e20.3	$⊢ χ \to (θ \to τ)$
4	2	vd02	$⊢ (φ, ψ \to θ)$
5	1 4 3	e22	$⊢ (φ, ψ \to τ)$