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Metamath Proof Explorer

Theorem brlmic

Description: The relation "is isomorphic to" for modules. (Contributed by Stefan O'Rear, 25-Jan-2015)

		Ref	Expression
	Assertion	brlmic	$⊢ R ≃_{𝑚} S \leftrightarrow R LMIso S \neq \emptyset$

Step	Hyp	Ref	Expression
1		df-lmic	$⊢ ≃_{𝑚} = {LMIso}^{-1} [V ∖ 1_{𝑜}]$
2		lmimfn	$⊢ LMIso Fn (LMod \times LMod)$
3	1 2	brwitnlem	$⊢ R ≃_{𝑚} S \leftrightarrow R LMIso S \neq \emptyset$