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Metamath Proof Explorer

Theorem dividOLD

Description: Obsolete version of divid as of 9-Jul-2025. (Contributed by NM, 1-Aug-2004) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	dividOLD	$⊢ (A \in ℂ \land A \neq 0) \to \frac{A}{A} = 1$

Proof

Step	Hyp	Ref	Expression
1		divrec	$⊢ (A \in ℂ \land A \in ℂ \land A \neq 0) \to \frac{A}{A} = A (\frac{1}{A})$
2	1	3anidm12	$⊢ (A \in ℂ \land A \neq 0) \to \frac{A}{A} = A (\frac{1}{A})$
3		recid	$⊢ (A \in ℂ \land A \neq 0) \to A (\frac{1}{A}) = 1$
4	2 3	eqtrd	$⊢ (A \in ℂ \land A \neq 0) \to \frac{A}{A} = 1$