Definition df-gic 19291

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.)

Assertion

Ref	Expression
df-gic	⊢ ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

Detailed syntax breakdown of Definition df-gic

Step	Hyp	Ref	Expression
1		cgic 19289	. 2 class ≃𝑔
2		cgim 19288	. . . 4 class GrpIso
3	2	ccnv 5642	. . 3 class ◡ GrpIso
4		cvv 3453	. . . 4 class V
5		c1o 8424	. . . 4 class 1o
6	4, 5	cdif 3899	. . 3 class (V ∖ 1o)
7	3, 6	cima 5646	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1559	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19301  gicer  19308