Theorem afv2prc

Description: A function's value at a proper class is not defined, compare with fvprc . (Contributed by AV, 5-Sep-2022)

	Ref	Expression
Assertion	afv2prc	⊢ ( ¬ 𝐴 ∈ V → ( 𝐹 '''' 𝐴 ) ∉ ran 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		prcnel	⊢ ( ¬ 𝐴 ∈ V → ¬ 𝐴 ∈ dom 𝐹 )
2		ndmafv2nrn	⊢ ( ¬ 𝐴 ∈ dom 𝐹 → ( 𝐹 '''' 𝐴 ) ∉ ran 𝐹 )
3	1 2	syl	⊢ ( ¬ 𝐴 ∈ V → ( 𝐹 '''' 𝐴 ) ∉ ran 𝐹 )