Metamath Proof Explorer


Theorem bnj1317

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

Ref Expression
Hypothesis bnj1317.1 𝐴 = { 𝑥𝜑 }
Assertion bnj1317 ( 𝑦𝐴 → ∀ 𝑥 𝑦𝐴 )

Proof

Step Hyp Ref Expression
1 bnj1317.1 𝐴 = { 𝑥𝜑 }
2 hbab1 ( 𝑦 ∈ { 𝑥𝜑 } → ∀ 𝑥 𝑦 ∈ { 𝑥𝜑 } )
3 1 2 hbxfreq ( 𝑦𝐴 → ∀ 𝑥 𝑦𝐴 )