Metamath Proof Explorer

Theorem rightold

Description: An element of a right set is an element of the old set. (Contributed by Scott Fenton, 27-Feb-2026)

Ref Expression
Assertion rightold 
|- ( A e. ( _Right ` B ) -> A e. ( _Old ` ( bday ` B ) ) )

Proof

Step Hyp Ref Expression
1 rightssold 
 |-  ( _Right ` B ) C_ ( _Old ` ( bday ` B ) )
2 1 sseli 
 |-  ( A e. ( _Right ` B ) -> A e. ( _Old ` ( bday ` B ) ) )