Theorem difexd

Description: Existence of a difference. (Contributed by SN, 16-Jul-2024)

	Ref	Expression
Hypothesis	difexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
Assertion	difexd	⊢ ( 𝜑 → ( 𝐴 ∖ 𝐵 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		difexd.1	⊢ ( 𝜑 → 𝐴 ∈ 𝑉 )
2		difexg	⊢ ( 𝐴 ∈ 𝑉 → ( 𝐴 ∖ 𝐵 ) ∈ V )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 ∖ 𝐵 ) ∈ V )