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Metamath Proof Explorer

Theorem exp520

Description: A triple exportation inference. (Contributed by Jeff Hankins, 8-Jul-2009)

		Ref	Expression
	Hypothesis	exp520.1	$⊢ ((φ \land ψ \land χ) \land (θ \land τ)) \to η$
	Assertion	exp520	$⊢ φ \to (ψ \to (χ \to (θ \to (τ \to η))))$

Step	Hyp	Ref	Expression
1		exp520.1	$⊢ ((φ \land ψ \land χ) \land (θ \land τ)) \to η$
2	1	ex	$⊢ (φ \land ψ \land χ) \to ((θ \land τ) \to η)$
3	2	exp5o	$⊢ φ \to (ψ \to (χ \to (θ \to (τ \to η))))$