Metamath Proof Explorer

Theorem wrecseq2

Description: Equality theorem for the well-founded recursive function generator. (Contributed by Scott Fenton, 7-Jun-2018)

Ref Expression
Assertion wrecseq2 
|- ( A = B -> wrecs ( R , A , F ) = wrecs ( R , B , F ) )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  R = R
2 eqid 
 |-  F = F
3 wrecseq123 
 |-  ( ( R = R /\ A = B /\ F = F ) -> wrecs ( R , A , F ) = wrecs ( R , B , F ) )
4 1 2 3 mp3an13 
 |-  ( A = B -> wrecs ( R , A , F ) = wrecs ( R , B , F ) )