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Metamath Proof Explorer

Theorem ee220

Description: e220 without virtual deductions. (Contributed by Alan Sare, 12-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee220.1	$⊢ φ \to (ψ \to χ)$
	ee220.2	$⊢ φ \to (ψ \to θ)$
	ee220.3	$⊢ τ$
	ee220.4	$⊢ χ \to (θ \to (τ \to η))$
Assertion	ee220	$⊢ φ \to (ψ \to η)$

Proof

Step	Hyp	Ref	Expression
1		ee220.1	$⊢ φ \to (ψ \to χ)$
2		ee220.2	$⊢ φ \to (ψ \to θ)$
3		ee220.3	$⊢ τ$
4		ee220.4	$⊢ χ \to (θ \to (τ \to η))$
5	3	2a1i	$⊢ φ \to (ψ \to τ)$
6	1 2 5 4	ee222	$⊢ φ \to (ψ \to η)$