Theorem uneq1i

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

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

Proof

Step	Hyp	Ref	Expression
1		uneq1i.1	⊢ 𝐴 = 𝐵
2		uneq1	⊢ ( 𝐴 = 𝐵 → ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 ) )
3	1 2	ax-mp	⊢ ( 𝐴 ∪ 𝐶 ) = ( 𝐵 ∪ 𝐶 )