Theorem fvprc

Description: A function's value at a proper class is the empty set. (Contributed by NM, 20-May-1998)

	Ref	Expression
Assertion	fvprc	⊢ ( ¬ 𝐴 ∈ V → ( 𝐹 ‘ 𝐴 ) = ∅ )

Proof

Step	Hyp	Ref	Expression
1		brprcneu	⊢ ( ¬ 𝐴 ∈ V → ¬ ∃! 𝑥 𝐴 𝐹 𝑥 )
2		tz6.12-2	⊢ ( ¬ ∃! 𝑥 𝐴 𝐹 𝑥 → ( 𝐹 ‘ 𝐴 ) = ∅ )
3	1 2	syl	⊢ ( ¬ 𝐴 ∈ V → ( 𝐹 ‘ 𝐴 ) = ∅ )