Theorem opabid2ss 32896

Description: One direction of opabid2 5813 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 23	. 2 ⊢ (⟨𝑥, 𝑦⟩ ∈ 𝐴 → ⟨𝑥, 𝑦⟩ ∈ 𝐴)
2	1	opabssi 32895	1 ⊢ {⟨𝑥, 𝑦⟩ ∣ ⟨𝑥, 𝑦⟩ ∈ 𝐴} ⊆ 𝐴

Syntax hints:   ∈ wcel 2149   ⊆ wss 3913  ⟨cop 4597  {copab 5174

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1570  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-ss 3930  df-opab 5175

This theorem is referenced by: (None)