Metamath Proof Explorer

Theorem wsuceq1

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

Ref Expression
Assertion wsuceq1 
|- ( R = S -> wsuc ( R , A , X ) = wsuc ( S , A , X ) )

Proof

Step Hyp Ref Expression
1 eqid 
 |-  A = A
2 eqid 
 |-  X = X
3 wsuceq123 
 |-  ( ( R = S /\ A = A /\ X = X ) -> wsuc ( R , A , X ) = wsuc ( S , A , X ) )
4 1 2 3 mp3an23 
 |-  ( R = S -> wsuc ( R , A , X ) = wsuc ( S , A , X ) )