Definition df-gic 19300

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 19298	. 2 class ≃𝑔
2		cgim 19297	. . . 4 class GrpIso
3	2	ccnv 5699	. . 3 class ◡ GrpIso
4		cvv 3488	. . . 4 class V
5		c1o 8515	. . . 4 class 1o
6	4, 5	cdif 3973	. . 3 class (V ∖ 1o)
7	3, 6	cima 5703	. 2 class (◡ GrpIso “ (V ∖ 1o))
8	1, 7	wceq 1537	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1o))

This definition is referenced by:  brgic  19310  gicer  19317