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Metamath Proof Explorer

Theorem bnj216

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj216.1 ⊢ B ∈ V
Assertion bnj216 ⊢ A = suc ⁡ B → B ∈ A

Proof

Step Hyp Ref Expression
1 bnj216.1 ⊢ B ∈ V
2 1 sucid ⊢ B ∈ suc ⁡ B
3 eleq2 ⊢ A = suc ⁡ B → B ∈ A ↔ B ∈ suc ⁡ B
4 2 3 mpbiri ⊢ A = suc ⁡ B → B ∈ A