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	⊢ ( ( 𝑈 ∈ Univ ∧ 𝑈 ∈ ∪ ( 𝑅1 “ On ) ) → 𝑈 = ( 𝑅1 ‘ ( 𝑈 ∩ On ) ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( 𝑈 ∩ On ) = ( 𝑈 ∩ On )
2	1	grur1	⊢ ( ( 𝑈 ∈ Univ ∧ 𝑈 ∈ ∪ ( 𝑅1 “ On ) ) → 𝑈 = ( 𝑅1 ‘ ( 𝑈 ∩ On ) ) )