Metamath Proof Explorer


Theorem wfrrel

Description: The well-ordered recursion generator generates a relation. Avoids the axiom of replacement. (Contributed by Scott Fenton, 8-Jun-2018) (Proof shortened by Scott Fenton, 17-Nov-2024)

Ref Expression
Hypothesis wfrrel.1
|- F = wrecs ( R , A , G )
Assertion wfrrel
|- Rel F

Proof

Step Hyp Ref Expression
1 wfrrel.1
 |-  F = wrecs ( R , A , G )
2 df-wrecs
 |-  wrecs ( R , A , G ) = frecs ( R , A , ( G o. 2nd ) )
3 1 2 eqtri
 |-  F = frecs ( R , A , ( G o. 2nd ) )
4 3 frrrel
 |-  Rel F