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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 ) )