Metamath Proof Explorer


Theorem sucexg

Description: The successor of a set is a set (generalization). (Contributed by NM, 5-Jun-1994)

Ref Expression
Assertion sucexg ⊢ A ∈ V → suc ⁡ A ∈ V

Proof

Step Hyp Ref Expression
1 elex ⊢ A ∈ V → A ∈ V
2 sucexb ⊢ A ∈ V ↔ suc ⁡ A ∈ V
3 1 2 sylib ⊢ A ∈ V → suc ⁡ A ∈ V