Theorem onnbtwn

Description: There is no set between an ordinal number and its successor. Proposition 7.25 of TakeutiZaring p. 41. (Contributed by NM, 9-Jun-1994)

	Ref	Expression
Assertion	onnbtwn	|- ( A e. On -> -. ( A e. B /\ B e. suc A ) )

Proof

Step	Hyp	Ref	Expression
1		eloni	|- ( A e. On -> Ord A )
2		ordnbtwn	|- ( Ord A -> -. ( A e. B /\ B e. suc A ) )
3	1 2	syl	|- ( A e. On -> -. ( A e. B /\ B e. suc A ) )