Definition df-gic 17525

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 17523	. 2 class ≃𝑔
2		cgim 17522	. . . 4 class GrpIso
3	2	ccnv 5037	. . 3 class ◡ GrpIso
4		cvv 3173	. . . 4 class V
5		c1o 7440	. . . 4 class 1𝑜
6	4, 5	cdif 3537	. . 3 class (V ∖ 1𝑜)
7	3, 6	cima 5041	. 2 class (◡ GrpIso “ (V ∖ 1𝑜))
8	1, 7	wceq 1475	1 wff ≃𝑔 = (◡ GrpIso “ (V ∖ 1𝑜))

This definition is referenced by:  brgic  17534  gicer  17541  gicerOLD  17542