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Theorem relsnop 5798
Description: A singleton of an ordered pair is a relation. (Contributed by NM, 17-May-1998.) (Revised by Mario Carneiro, 26-Apr-2015.)
Hypotheses
Ref Expression
relsn.1 𝐴 ∈ V
relsnop.2 𝐵 ∈ V
Assertion
Ref Expression
relsnop Rel {⟨𝐴, 𝐵⟩}

Proof of Theorem relsnop
StepHypRef Expression
1 relsn.1 . 2 𝐴 ∈ V
2 relsnop.2 . 2 𝐵 ∈ V
3 relsnopg 5796 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → Rel {⟨𝐴, 𝐵⟩})
41, 2, 3mp2an 689 1 Rel {⟨𝐴, 𝐵⟩}
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  Vcvv 3468  {csn 4623  cop 4629  Rel wrel 5674
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-sep 5292  ax-nul 5299  ax-pr 5420
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-ral 3056  df-rex 3065  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-opab 5204  df-xp 5675  df-rel 5676
This theorem is referenced by:  fsn  7128  imasaddfnlem  17481  ex-res  30199
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