Theorem afvprc

Description: A function's value at a proper class is the universe, compare with fvprc . (Contributed by Alexander van der Vekens, 25-May-2017)

	Ref	Expression
Assertion	afvprc	⊢ ( ¬ 𝐴 ∈ V → ( 𝐹 ''' 𝐴 ) = V )

Proof

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