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Metamath Proof Explorer

Theorem suceq

Description: Equality of successors. (Contributed by NM, 30-Aug-1993) (Proof shortened by Andrew Salmon, 25-Jul-2011)

Ref Expression
Assertion suceq ( 𝐴 = 𝐵 → suc 𝐴 = suc 𝐵 )

Proof

Step Hyp Ref Expression
1 id ⊢ ( 𝐴 = 𝐵 → 𝐴 = 𝐵 )
2 1 suceqd ⊢ ( 𝐴 = 𝐵 → suc 𝐴 = suc 𝐵 )