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Theorem relsnopOLD 5368
 Description: Obsolete proof of relsnop 5367 as of 12-Feb-2022. (Contributed by NM, 17-May-1998.) (Revised by Mario Carneiro, 26-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
relsn.1 𝐴 ∈ V
relsnop.2 𝐵 ∈ V
Assertion
Ref Expression
relsnopOLD Rel {⟨𝐴, 𝐵⟩}

Proof of Theorem relsnopOLD
StepHypRef Expression
1 relsn.1 . . 3 𝐴 ∈ V
2 relsnop.2 . . 3 𝐵 ∈ V
31, 2opelvv 5306 . 2 𝐴, 𝐵⟩ ∈ (V × V)
4 opex 5060 . . 3 𝐴, 𝐵⟩ ∈ V
54relsn 5365 . 2 (Rel {⟨𝐴, 𝐵⟩} ↔ ⟨𝐴, 𝐵⟩ ∈ (V × V))
63, 5mpbir 221 1 Rel {⟨𝐴, 𝐵⟩}
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 2145  Vcvv 3351  {csn 4316  ⟨cop 4322   × cxp 5247  Rel wrel 5254 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751  ax-sep 4915  ax-nul 4923  ax-pr 5034 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 835  df-3an 1073  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-rab 3070  df-v 3353  df-dif 3726  df-un 3728  df-in 3730  df-ss 3737  df-nul 4064  df-if 4226  df-sn 4317  df-pr 4319  df-op 4323  df-opab 4847  df-xp 5255  df-rel 5256 This theorem is referenced by: (None)
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