Theorem uneq2i

Description: Inference adding union to the left in a class equality. (Contributed by NM, 30-Aug-1993)

	Ref	Expression
Hypothesis	uneq1i.1	⊢ 𝐴 = 𝐵
Assertion	uneq2i	⊢ ( 𝐶 ∪ 𝐴 ) = ( 𝐶 ∪ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		uneq1i.1	⊢ 𝐴 = 𝐵
2		uneq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ∪ 𝐴 ) = ( 𝐶 ∪ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 ∪ 𝐴 ) = ( 𝐶 ∪ 𝐵 )