Definition df-gic

Description: Two groups are said to be isomorphic iff they are connected by at least one isomorphism. Isomorphic groups share all global group properties, but to relate local properties requires knowledge of a specific isomorphism. (Contributed by Stefan O'Rear, 25-Jan-2015)

	Ref	Expression
Assertion	df-gic	$$⊢{\simeq }_{𝑔}={\mathrm{GrpIso}}^{-1}\left[\mathrm{V}\setminus 1_{𝑜}\right]$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgic	$$class{\simeq }_{𝑔}$$
1		cgim	$$class\mathrm{GrpIso}$$
2	1	ccnv	$$class{\mathrm{GrpIso}}^{-1}$$
3		cvv	$$class\mathrm{V}$$
4		c1o	$$class{1}_{𝑜}$$
5	3 4	cdif	$$class\left(\mathrm{V}\setminus 1_{𝑜}\right)$$
6	2 5	cima	$$class{\mathrm{GrpIso}}^{-1}\left[\mathrm{V}\setminus 1_{𝑜}\right]$$
7	0 6	wceq	$$wff{\simeq }_{𝑔}={\mathrm{GrpIso}}^{-1}\left[\mathrm{V}\setminus 1_{𝑜}\right]$$