Metamath Proof Explorer

Theorem recsval

Description: Strong transfinite recursion in terms of all previous values. (Contributed by Stefan O'Rear, 18-Jan-2015)

Ref Expression
Assertion recsval 
|- ( A e. On -> ( recs ( F ) ` A ) = ( F ` ( recs ( F ) |` A ) ) )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  recs ( F ) = recs ( F )
2 1 tfr2 
 |-  ( A e. On -> ( recs ( F ) ` A ) = ( F ` ( recs ( F ) |` A ) ) )