Theorem trwf

Description: The class of well-founded sets is transitive. (Contributed by Eric Schmidt, 9-Sep-2025)

	Ref	Expression
Assertion	trwf	|- Tr U. ( R1 " On )

Proof

Step	Hyp	Ref	Expression
1		r1elssi	|- ( x e. U. ( R1 " On ) -> x C_ U. ( R1 " On ) )
2	1	rgen	|- A. x e. U. ( R1 " On ) x C_ U. ( R1 " On )
3		dftr3	|- ( Tr U. ( R1 " On ) <-> A. x e. U. ( R1 " On ) x C_ U. ( R1 " On ) )
4	2 3	mpbir	|- Tr U. ( R1 " On )