Theorem opabid2ss 32561

Description: One direction of opabid2 5818 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 32560	1 ⊢ {⟨𝑥, 𝑦⟩ ∣ ⟨𝑥, 𝑦⟩ ∈ 𝐴} ⊆ 𝐴

Syntax hints:   ∈ wcel 2107   ⊆ wss 3931  ⟨cop 4612  {copab 5185

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2713  df-cleq 2726  df-clel 2808  df-ss 3948  df-opab 5186

This theorem is referenced by: (None)