Theorem bnj1113

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bnj1113.1	⊢ ( 𝐴 = 𝐵 → 𝐶 = 𝐷 )
Assertion	bnj1113	⊢ ( 𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸 )

Proof

Step	Hyp	Ref	Expression
1		bnj1113.1	⊢ ( 𝐴 = 𝐵 → 𝐶 = 𝐷 )
2	1	iuneq1d	⊢ ( 𝐴 = 𝐵 → ∪ 𝑥 ∈ 𝐶 𝐸 = ∪ 𝑥 ∈ 𝐷 𝐸 )