Theorem scott0bOLD

Description: Obsolete version of scott0b as of 18-Jul-2026. (Contributed by BTernaryTau, 3-Jul-2026) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	scott0bOLD	|- ( A = (/) <-> Scott A = (/) )

Proof

Step	Hyp	Ref	Expression
1		scott0OLD	|- ( A = (/) <-> { x e. A | A. y e. A ( rank ` x ) C_ ( rank ` y ) } = (/) )
2		df-scott	|- Scott A = { x e. A | A. y e. A ( rank ` x ) C_ ( rank ` y ) }
3	2	eqeq1i	|- ( Scott A = (/) <-> { x e. A | A. y e. A ( rank ` x ) C_ ( rank ` y ) } = (/) )
4	1 3	bitr4i	|- ( A = (/) <-> Scott A = (/) )