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Metamath Proof Explorer

Theorem imp4b

Description: An importation inference. (Contributed by NM, 26-Apr-1994) Shorten imp4a . (Revised by Wolf Lammen, 19-Jul-2021)

		Ref	Expression
	Hypothesis	imp4.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
	Assertion	imp4b	$⊢ (φ \land ψ) \to ((χ \land θ) \to τ)$

Step	Hyp	Ref	Expression
1		imp4.1	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
2	1	imp	$⊢ (φ \land ψ) \to (χ \to (θ \to τ))$
3	2	impd	$⊢ (φ \land ψ) \to ((χ \land θ) \to τ)$