Theorem isomgrref

Description: The isomorphy relation is reflexive for hypergraphs. (Contributed by AV, 11-Nov-2022)

	Ref	Expression
Assertion	isomgrref	⊢ ( 𝐺 ∈ UHGraph → 𝐺 IsomGr 𝐺 )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝐺 ∈ UHGraph → 𝐺 ∈ UHGraph )
2		eqid	⊢ ( Vtx ‘ 𝐺 ) = ( Vtx ‘ 𝐺 )
3		eqid	⊢ ( iEdg ‘ 𝐺 ) = ( iEdg ‘ 𝐺 )
4	2 3	pm3.2i	⊢ ( ( Vtx ‘ 𝐺 ) = ( Vtx ‘ 𝐺 ) ∧ ( iEdg ‘ 𝐺 ) = ( iEdg ‘ 𝐺 ) )
5	4	a1i	⊢ ( 𝐺 ∈ UHGraph → ( ( Vtx ‘ 𝐺 ) = ( Vtx ‘ 𝐺 ) ∧ ( iEdg ‘ 𝐺 ) = ( iEdg ‘ 𝐺 ) ) )
6		isomgreqve	⊢ ( ( ( 𝐺 ∈ UHGraph ∧ 𝐺 ∈ UHGraph ) ∧ ( ( Vtx ‘ 𝐺 ) = ( Vtx ‘ 𝐺 ) ∧ ( iEdg ‘ 𝐺 ) = ( iEdg ‘ 𝐺 ) ) ) → 𝐺 IsomGr 𝐺 )
7	1 1 5 6	syl21anc	⊢ ( 𝐺 ∈ UHGraph → 𝐺 IsomGr 𝐺 )