Theorem rightirr

Description: No surreal is a member of its right set. (Contributed by Scott Fenton, 20-Aug-2024)

	Ref	Expression
Assertion	rightirr	|- ( X e. No -> -. X e. ( _R ` X ) )

Proof

Step	Hyp	Ref	Expression
1		oldirr	|- -. X e. ( _Old ` ( bday ` X ) )
2		rightssold	|- ( X e. No -> ( _R ` X ) C_ ( _Old ` ( bday ` X ) ) )
3	2	sseld	|- ( X e. No -> ( X e. ( _R ` X ) -> X e. ( _Old ` ( bday ` X ) ) ) )
4	1 3	mtoi	|- ( X e. No -> -. X e. ( _R ` X ) )