Metamath Proof Explorer


Theorem onsucss

Description: If one ordinal is less than another, then the successor of the first is less than or equal to the second. Lemma 1.13 of Schloeder p. 2. See ordsucss . (Contributed by RP, 16-Jan-2025)

Ref Expression
Assertion onsucss A On B A suc B A

Proof

Step Hyp Ref Expression
1 eloni A On Ord A
2 ordsucss Ord A B A suc B A
3 1 2 syl A On B A suc B A