Metamath Proof Explorer


Theorem onunisuci

Description: An ordinal number is equal to the union of its successor. (Contributed by NM, 12-Jun-1994)

Ref Expression
Hypothesis on.1
|- A e. On
Assertion onunisuci
|- U. suc A = A

Proof

Step Hyp Ref Expression
1 on.1
 |-  A e. On
2 onunisuc
 |-  ( A e. On -> U. suc A = A )
3 1 2 ax-mp
 |-  U. suc A = A