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Metamath Proof Explorer

Theorem idsymrel

Description: The identity relation is symmetric. (Contributed by AV, 19-Jun-2022)

		Ref	Expression
	Assertion	idsymrel	⊢ SymRel I

Step	Hyp	Ref	Expression
1		cnvi	⊢ ^◡ I = I
2		reli	⊢ Rel I
3		dfsymrel4	⊢ ( SymRel I ↔ ( ^◡ I = I ∧ Rel I ) )
4	1 2 3	mpbir2an	⊢ SymRel I