Theorem uneq12i

Description: Equality inference for the union of two classes. (Contributed by NM, 12-Aug-2004) (Proof shortened by Eric Schmidt, 26-Jan-2007)

	Ref	Expression
Hypotheses	uneq1i.1	$$⊢A=B$$
	uneq12i.2	$$⊢C=D$$
Assertion	uneq12i	$$⊢A\cup C=B\cup D$$

Proof

Step	Hyp	Ref	Expression
1		uneq1i.1	$$⊢A=B$$
2		uneq12i.2	$$⊢C=D$$
3		uneq12	$$⊢\left(A=B\wedge C=D\right)\to A\cup C=B\cup D$$
4	1 2 3	mp2an	$$⊢A\cup C=B\cup D$$