Theorem unieqd

Description: Deduction of equality of two class unions. (Contributed by NM, 21-Apr-1995)

	Ref	Expression
Hypothesis	unieqd.1	$$⊢\phi \to A=B$$
Assertion	unieqd	$$⊢\phi \to \bigcup A=\bigcup B$$

Proof

Step	Hyp	Ref	Expression
1		unieqd.1	$$⊢\phi \to A=B$$
2		unieq	$$⊢A=B\to \bigcup A=\bigcup B$$
3	1 2	syl	$$⊢\phi \to \bigcup A=\bigcup B$$