Metamath Proof Explorer


Theorem bnj1436

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

Ref Expression
Hypothesis bnj1436.1 ⊢ 𝐴 = { 𝑥 ∣ 𝜑 }
Assertion bnj1436 ( 𝑥 ∈ 𝐴 → 𝜑 )

Proof

Step Hyp Ref Expression
1 bnj1436.1 ⊢ 𝐴 = { 𝑥 ∣ 𝜑 }
2 1 eqabri ⊢ ( 𝑥 ∈ 𝐴 ↔ 𝜑 )
3 2 biimpi ⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )