Theorem unieqi

Description: Inference of equality of two class unions. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	unieqi.1	⊢ 𝐴 = 𝐵
Assertion	unieqi	⊢ ∪ 𝐴 = ∪ 𝐵

Proof

Step	Hyp	Ref	Expression
1		unieqi.1	⊢ 𝐴 = 𝐵
2		unieq	⊢ ( 𝐴 = 𝐵 → ∪ 𝐴 = ∪ 𝐵 )
3	1 2	ax-mp	⊢ ∪ 𝐴 = ∪ 𝐵