Theorem unieqOLD

Description: Obsolete version of unieq as of 13-Apr-2024. (Contributed by NM, 10-Aug-1993) (Proof modification is discouraged.) (New usage is discouraged.) 29-Jun-2011.)

	Ref	Expression
Assertion	unieqOLD	$$⊢A=B\to \bigcup A=\bigcup B$$

Proof

Step	Hyp	Ref	Expression
1		rexeq	$$⊢A=B\to \left(\exists x\in Ay\in x\leftrightarrow \exists x\in By\in x\right)$$
2	1	abbidv	$$⊢A=B\to \left\{y|\exists x\in Ay\in x\right\}=\left\{y|\exists x\in By\in x\right\}$$
3		dfuni2	$$⊢\bigcup A=\left\{y|\exists x\in Ay\in x\right\}$$
4		dfuni2	$$⊢\bigcup B=\left\{y|\exists x\in By\in x\right\}$$
5	2 3 4	3eqtr4g	$$⊢A=B\to \bigcup A=\bigcup B$$