Theorem relopabvOLD 5804

Description: Obsolete version of relopab 5808 as of 26-Oct-2026. (Contributed by SN, 8-Sep-2024.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
relopabvOLD	⊢ Rel {⟨𝑥, 𝑦⟩ ∣ 𝜑}

Distinct variable group:   𝑥,𝑦

Allowed substitution hints:   𝜑(𝑥, 𝑦)

Proof of Theorem relopabvOLD

Step	Hyp	Ref	Expression
1		eqid 2763	. 2 ⊢ {⟨𝑥, 𝑦⟩ ∣ 𝜑} = {⟨𝑥, 𝑦⟩ ∣ 𝜑}
2	1	relopabiv 5803	1 ⊢ Rel {⟨𝑥, 𝑦⟩ ∣ 𝜑}

This proof depends on syntax axioms:  {copab 5170  Rel wrel 5660

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-opab 5171  df-xp 5661  df-rel 5662

This theorem is used by: (None)