Theorem bnj1538

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

	Ref	Expression
Hypothesis	bnj1538.1	⊢ 𝐴 = { 𝑥 ∈ 𝐵 ∣ 𝜑 }
Assertion	bnj1538	⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		bnj1538.1	⊢ 𝐴 = { 𝑥 ∈ 𝐵 ∣ 𝜑 }
2	1	rabeq2i	⊢ ( 𝑥 ∈ 𝐴 ↔ ( 𝑥 ∈ 𝐵 ∧ 𝜑 ) )
3	2	simprbi	⊢ ( 𝑥 ∈ 𝐴 → 𝜑 )