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Metamath Proof Explorer

Theorem sucid

Description: A set belongs to its successor. (Contributed by NM, 22-Jun-1994) (Proof shortened by Alan Sare, 18-Feb-2012) (Proof shortened by Scott Fenton, 20-Feb-2012)

Ref Expression
Hypothesis sucid.1 ⊢ A ∈ V
Assertion sucid ⊢ A ∈ suc ⁡ A

Proof

Step Hyp Ref Expression
1 sucid.1 ⊢ A ∈ V
2 sucidg ⊢ A ∈ V → A ∈ suc ⁡ A
3 1 2 ax-mp ⊢ A ∈ suc ⁡ A