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Theorem unipr 4925
Description: The union of a pair is the union of its members. Proposition 5.7 of [TakeutiZaring] p. 16. (Contributed by NM, 23-Aug-1993.) (Proof shortened by BJ, 1-Sep-2024.)
Hypotheses
Ref Expression
unipr.1 𝐴 ∈ V
unipr.2 𝐵 ∈ V
Assertion
Ref Expression
unipr {𝐴, 𝐵} = (𝐴𝐵)

Proof of Theorem unipr
StepHypRef Expression
1 unipr.1 . 2 𝐴 ∈ V
2 unipr.2 . 2 𝐵 ∈ V
3 uniprg 4924 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → {𝐴, 𝐵} = (𝐴𝐵))
41, 2, 3mp2an 691 1 {𝐴, 𝐵} = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534  wcel 2099  Vcvv 3471  cun 3945  {cpr 4631   cuni 4908
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-un 3952  df-sn 4630  df-pr 4632  df-uni 4909
This theorem is referenced by:  uniprgOLD  4927  uniintsn  4990  uniop  5517  unex  7748  nlim2  8510  rankxplim  9902  mrcun  17601  indistps  22913  indistps2  22914  leordtval2  23115  ex-uni  30235  mnuprdlem1  43709  mnuprdlem2  43710  mnurndlem1  43718  fouriersw  45619
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