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Metamath Proof Explorer

Theorem funrel

Description: A function is a relation. (Contributed by NM, 1-Aug-1994)

		Ref	Expression
	Assertion	funrel	⊢ ( Fun 𝐴 → Rel 𝐴 )

Step	Hyp	Ref	Expression
1		df-fun	⊢ ( Fun 𝐴 ↔ ( Rel 𝐴 ∧ ( 𝐴 ∘ ^◡ 𝐴 ) ⊆ I ) )
2	1	simplbi	⊢ ( Fun 𝐴 → Rel 𝐴 )