Metamath Proof Explorer

Theorem wsuceq2

Description: Equality theorem for well-founded successor. (Contributed by Scott Fenton, 13-Jun-2018)

Ref Expression
Assertion wsuceq2 
|- ( A = B -> wsuc ( R , A , X ) = wsuc ( R , B , X ) )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  R = R
2 eqid 
 |-  X = X
3 wsuceq123 
 |-  ( ( R = R /\ A = B /\ X = X ) -> wsuc ( R , A , X ) = wsuc ( R , B , X ) )
4 1 2 3 mp3an13 
 |-  ( A = B -> wsuc ( R , A , X ) = wsuc ( R , B , X ) )