Theorem iuneq1i

Description: Equality theorem for indexed union. (Contributed by Glauco Siliprandi, 3-Mar-2021)

	Ref	Expression
Hypothesis	iuneq1i.1	⊢ 𝐴 = 𝐵
Assertion	iuneq1i	⊢ ∪ 𝑥 ∈ 𝐴 𝐶 = ∪ 𝑥 ∈ 𝐵 𝐶

Proof

Step	Hyp	Ref	Expression
1		iuneq1i.1	⊢ 𝐴 = 𝐵
2		iuneq1	⊢ ( 𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐴 𝐶 = ∪ 𝑥 ∈ 𝐵 𝐶 )
3	1 2	ax-mp	⊢ ∪ 𝑥 ∈ 𝐴 𝐶 = ∪ 𝑥 ∈ 𝐵 𝐶