Definition df-gic 18664

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 18662	. 2 class ≃𝑔
2		cgim 18661	. . . 4 class GrpIso
3	2	ccnv 5550	. . 3 class ◡ GrpIso
4		cvv 3408	. . . 4 class V
5		c1o 8195	. . . 4 class 1o
6	4, 5	cdif 3863	. . 3 class (V ∖ 1o)
7	3, 6	cima 5554	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1543	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  18673  gicer  18680