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Metamath Proof Explorer

Theorem brgici

Description: Prove isomorphic by an explicit isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015)

		Ref	Expression
	Assertion	brgici	$⊢ F \in (R GrpIso S) \to R ≃_{𝑔} S$

Step	Hyp	Ref	Expression
1		ne0i	$⊢ F \in (R GrpIso S) \to R GrpIso S \neq \emptyset$
2		brgic	$⊢ R ≃_{𝑔} S \leftrightarrow R GrpIso S \neq \emptyset$
3	1 2	sylibr	$⊢ F \in (R GrpIso S) \to R ≃_{𝑔} S$