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Metamath Proof Explorer

Theorem ee33an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee33an.1	$⊢ φ \to (ψ \to (χ \to θ))$
	ee33an.2	$⊢ φ \to (ψ \to (χ \to τ))$
	ee33an.3	$⊢ (θ \land τ) \to η$
Assertion	ee33an	$⊢ φ \to (ψ \to (χ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee33an.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		ee33an.2	$⊢ φ \to (ψ \to (χ \to τ))$
3		ee33an.3	$⊢ (θ \land τ) \to η$
4	3	ex	$⊢ θ \to (τ \to η)$
5	1 2 4	ee33	$⊢ φ \to (ψ \to (χ \to η))$