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Metamath Proof Explorer

Theorem eel0000

Description: Elimination rule similar to mp4an , except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017)

	Ref	Expression
Hypotheses	eel0000.1	$⊢ φ$
	eel0000.2	$⊢ ψ$
	eel0000.3	$⊢ χ$
	eel0000.4	$⊢ θ$
	eel0000.5	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$
Assertion	eel0000	$⊢ τ$

Proof

Step	Hyp	Ref	Expression
1		eel0000.1	$⊢ φ$
2		eel0000.2	$⊢ ψ$
3		eel0000.3	$⊢ χ$
4		eel0000.4	$⊢ θ$
5		eel0000.5	$⊢ (((φ \land ψ) \land χ) \land θ) \to τ$
6	5	exp41	$⊢ φ \to (ψ \to (χ \to (θ \to τ)))$
7	1 2 6	mp2	$⊢ χ \to (θ \to τ)$
8	3 4 7	mp2	$⊢ τ$