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