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Metamath Proof Explorer

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	\|- ~=g = ( `' GrpIso " ( _V \ 1o ) )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cgic	\|- ~=g
1		cgim	\|- GrpIso
2	1	ccnv	\|- `' GrpIso
3		cvv	\|- _V
4		c1o	\|- 1o
5	3 4	cdif	\|- ( _V \ 1o )
6	2 5	cima	\|- ( `' GrpIso " ( _V \ 1o ) )
7	0 6	wceq	\|- ~=g = ( `' GrpIso " ( _V \ 1o ) )