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Metamath Proof Explorer

Theorem e3

Description: Meta-connective form of syl8 . (Contributed by Alan Sare, 15-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e3.1	$⊢ (φ, ψ, χ \to θ)$
	e3.2	$⊢ θ \to τ$
Assertion	e3	$⊢ (φ, ψ, χ \to τ)$

Proof

Step	Hyp	Ref	Expression
1		e3.1	$⊢ (φ, ψ, χ \to θ)$
2		e3.2	$⊢ θ \to τ$
3	2	a1i	$⊢ θ \to (θ \to τ)$
4	1 1 3	e33	$⊢ (φ, ψ, χ \to τ)$