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Metamath Proof Explorer

Theorem ee23an

Description: e23an without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ee23an.1	$⊢ φ \to (ψ \to χ)$
	ee23an.2	$⊢ φ \to (ψ \to (θ \to τ))$
	ee23an.3	$⊢ (χ \land τ) \to η$
Assertion	ee23an	$⊢ φ \to (ψ \to (θ \to η))$

Proof

Step	Hyp	Ref	Expression
1		ee23an.1	$⊢ φ \to (ψ \to χ)$
2		ee23an.2	$⊢ φ \to (ψ \to (θ \to τ))$
3		ee23an.3	$⊢ (χ \land τ) \to η$
4	1	a1dd	$⊢ φ \to (ψ \to (θ \to χ))$
5	4 2 3	ee33an	$⊢ φ \to (ψ \to (θ \to η))$