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Metamath Proof Explorer

Theorem elsuc2

Description: Membership in a successor. (Contributed by NM, 15-Sep-2003)

Ref Expression
Hypothesis elsuc.1 ⊢ A ∈ V
Assertion elsuc2 ⊢ B ∈ suc ⁡ A ↔ B ∈ A ∨ B = A

Proof

Step Hyp Ref Expression
1 elsuc.1 ⊢ A ∈ V
2 elsuc2g ⊢ A ∈ V → B ∈ suc ⁡ A ↔ B ∈ A ∨ B = A
3 1 2 ax-mp ⊢ B ∈ suc ⁡ A ↔ B ∈ A ∨ B = A