Theorem opabid2ss 32777

Description: One direction of opabid2 5797 which holds without a Rel 𝐴 requirement. (Contributed by Thierry Arnoux, 18-Feb-2022.)

Assertion

Ref	Expression
opabid2ss	⊢ {⟨𝑥, 𝑦⟩ ∣ ⟨𝑥, 𝑦⟩ ∈ 𝐴} ⊆ 𝐴

Distinct variable group:   𝑥,𝐴,𝑦

Proof of Theorem opabid2ss

Step	Hyp	Ref	Expression
1		id 22	. 2 ⊢ (⟨𝑥, 𝑦⟩ ∈ 𝐴 → ⟨𝑥, 𝑦⟩ ∈ 𝐴)
2	1	opabssi 32776	1 ⊢ {⟨𝑥, 𝑦⟩ ∣ ⟨𝑥, 𝑦⟩ ∈ 𝐴} ⊆ 𝐴

Syntax hints:   ∈ wcel 2141   ⊆ wss 3902  ⟨cop 4585  {copab 5159

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-ss 3919  df-opab 5160

This theorem is referenced by: (None)