Metamath Proof Explorer

Theorem leftold

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

Ref Expression
Assertion leftold 
|- ( A e. ( _Left ` B ) -> A e. ( _Old ` ( bday ` B ) ) )

Proof

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