Theorem imanonrel

Description: An image under the non-relation part of a class is empty. (Contributed by RP, 22-Oct-2020)

	Ref	Expression
Assertion	imanonrel	⊢ ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) “ 𝐵 ) = ∅

Proof

Step	Hyp	Ref	Expression
1		df-ima	⊢ ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) “ 𝐵 ) = ran ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) ↾ 𝐵 )
2		resnonrel	⊢ ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) ↾ 𝐵 ) = ∅
3	2	rneqi	⊢ ran ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) ↾ 𝐵 ) = ran ∅
4		rn0	⊢ ran ∅ = ∅
5	1 3 4	3eqtri	⊢ ( ( 𝐴 ∖ ◡ ◡ 𝐴 ) “ 𝐵 ) = ∅