Theorem fundif

Description: A function with removed elements is still a function. (Contributed by AV, 7-Jun-2021) Shorten proof and remove dependency on ax-sep and ax-pr . (Revised by Eric Schmidt, 24-Oct-2026)

	Ref	Expression
Assertion	fundif	⊢ ( Fun 𝐹 → Fun ( 𝐹 ∖ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		difss	⊢ ( 𝐹 ∖ 𝐴 ) ⊆ 𝐹
2		funss	⊢ ( ( 𝐹 ∖ 𝐴 ) ⊆ 𝐹 → ( Fun 𝐹 → Fun ( 𝐹 ∖ 𝐴 ) ) )
3	1 2	ax-mp	⊢ ( Fun 𝐹 → Fun ( 𝐹 ∖ 𝐴 ) )