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Metamath Proof Explorer

Theorem ee13

Description: e13 without virtual deduction connectives. Special theorem needed for the Virtual Deduction translation tool. (Contributed by Alan Sare, 28-Oct-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee13.1	$⊢ φ \to ψ$
	ee13.2	$⊢ φ \to (χ \to (θ \to τ))$
	ee13.3	$⊢ ψ \to (τ \to η)$
Assertion	ee13	$⊢ φ \to (χ \to (θ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee13.1	$⊢ φ \to ψ$
2		ee13.2	$⊢ φ \to (χ \to (θ \to τ))$
3		ee13.3	$⊢ ψ \to (τ \to η)$
4	1 3	syl	$⊢ φ \to (τ \to η)$
5	2 4	syl6d	$⊢ φ \to (χ \to (θ \to η))$