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 𝐵𝐵𝐴 )

Proof

Step Hyp Ref Expression
1 bnj216.1 𝐵 ∈ V
2 1 sucid 𝐵 ∈ suc 𝐵
3 eleq2 ( 𝐴 = suc 𝐵 → ( 𝐵𝐴𝐵 ∈ suc 𝐵 ) )
4 2 3 mpbiri ( 𝐴 = suc 𝐵𝐵𝐴 )