Theorem rabex2OLD 4744

Description: Obsolete version of rabex2 4742 as of 26-Mar-2021. (Contributed by AV, 16-Jul-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypotheses

Ref	Expression
rabex2OLD.1	⊢ 𝐵 = {𝑥 ∈ 𝐴 ∣ 𝜓}
rabex2OLD.2	⊢ 𝐴 ∈ 𝑉

Assertion

Ref	Expression
rabex2OLD	⊢ 𝐵 ∈ V

Distinct variable group:   𝑥,𝐴

Allowed substitution hints:   𝜓(𝑥)   𝐵(𝑥)   𝑉(𝑥)

Proof of Theorem rabex2OLD

Step	Hyp	Ref	Expression
1		rabex2OLD.2	. 2 ⊢ 𝐴 ∈ 𝑉
2		rabex2OLD.1	. . 3 ⊢ 𝐵 = {𝑥 ∈ 𝐴 ∣ 𝜓}
3		id 22	. . 3 ⊢ (𝐴 ∈ 𝑉 → 𝐴 ∈ 𝑉)
4	2, 3	rabexd 4741	. 2 ⊢ (𝐴 ∈ 𝑉 → 𝐵 ∈ V)
5	1, 4	ax-mp 5	1 ⊢ 𝐵 ∈ V

Syntax hints:   = wceq 1475   ∈ wcel 1977  {crab 2900  Vcvv 3173

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rab 2905  df-v 3175  df-in 3547  df-ss 3554

This theorem is referenced by:  rab2exOLD  4745