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Theorem cnvsnOLD 5762
Description: Obsolete proof of cnvsn 5761 as of 12-Feb-2022. (Contributed by NM, 11-May-1998.) (Revised by Mario Carneiro, 26-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
cnvsn.1 𝐴 ∈ V
cnvsn.2 𝐵 ∈ V
Assertion
Ref Expression
cnvsnOLD {⟨𝐴, 𝐵⟩} = {⟨𝐵, 𝐴⟩}

Proof of Theorem cnvsnOLD
StepHypRef Expression
1 cnvcnvsn 5754 . 2 {⟨𝐵, 𝐴⟩} = {⟨𝐴, 𝐵⟩}
2 cnvsn.2 . . . 4 𝐵 ∈ V
3 cnvsn.1 . . . 4 𝐴 ∈ V
42, 3relsnop 5367 . . 3 Rel {⟨𝐵, 𝐴⟩}
5 dfrel2 5724 . . 3 (Rel {⟨𝐵, 𝐴⟩} ↔ {⟨𝐵, 𝐴⟩} = {⟨𝐵, 𝐴⟩})
64, 5mpbi 220 . 2 {⟨𝐵, 𝐴⟩} = {⟨𝐵, 𝐴⟩}
71, 6eqtr3i 2794 1 {⟨𝐴, 𝐵⟩} = {⟨𝐵, 𝐴⟩}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1630  wcel 2144  Vcvv 3349  {csn 4314  cop 4320  ccnv 5248  Rel wrel 5254
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1990  ax-6 2056  ax-7 2092  ax-9 2153  ax-10 2173  ax-11 2189  ax-12 2202  ax-13 2407  ax-ext 2750  ax-sep 4912  ax-nul 4920  ax-pr 5034
This theorem depends on definitions:  df-bi 197  df-an 383  df-or 827  df-3an 1072  df-tru 1633  df-ex 1852  df-nf 1857  df-sb 2049  df-eu 2621  df-mo 2622  df-clab 2757  df-cleq 2763  df-clel 2766  df-nfc 2901  df-ral 3065  df-rex 3066  df-rab 3069  df-v 3351  df-dif 3724  df-un 3726  df-in 3728  df-ss 3735  df-nul 4062  df-if 4224  df-sn 4315  df-pr 4317  df-op 4321  df-br 4785  df-opab 4845  df-xp 5255  df-rel 5256  df-cnv 5257
This theorem is referenced by: (None)
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