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Metamath Proof Explorer

Theorem ee32an

Description: e33an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee32an.1	$⊢ φ \to (ψ \to (χ \to θ))$
	ee32an.2	$⊢ φ \to (ψ \to τ)$
	ee32an.3	$⊢ (θ \land τ) \to η$
Assertion	ee32an	$⊢ φ \to (ψ \to (χ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee32an.1	$⊢ φ \to (ψ \to (χ \to θ))$
2		ee32an.2	$⊢ φ \to (ψ \to τ)$
3		ee32an.3	$⊢ (θ \land τ) \to η$
4	2	a1dd	$⊢ φ \to (ψ \to (χ \to τ))$
5	1 4 3	ee33an	$⊢ φ \to (ψ \to (χ \to η))$