Theorem bj-grur1

Description: Remove hypothesis from grur1 . Illustration of how to remove a "definitional hypothesis". This makes its uses longer, but the theorem feels more self-contained. It looks preferable when the defined term appears only once in the conclusion. (Contributed by BJ, 14-Sep-2019)

	Ref	Expression
Assertion	bj-grur1	$$⊢\left(U\in \mathrm{Univ}\wedge U\in \bigcup R_1\left[\mathrm{On}\right]\right)\to U=R_1\left(U\cap \mathrm{On}\right)$$

Proof

Step	Hyp	Ref	Expression
1		eqid	$$⊢U\cap \mathrm{On}=U\cap \mathrm{On}$$
2	1	grur1	$$⊢\left(U\in \mathrm{Univ}\wedge U\in \bigcup R_1\left[\mathrm{On}\right]\right)\to U=R_1\left(U\cap \mathrm{On}\right)$$