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Theorem unipr 4917
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 4916 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → {𝐴, 𝐵} = (𝐴𝐵))
41, 2, 3mp2an 689 1 {𝐴, 𝐵} = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  wcel 2098  Vcvv 3466  cun 3939  {cpr 4623   cuni 4900
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 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-un 3946  df-sn 4622  df-pr 4624  df-uni 4901
This theorem is referenced by:  uniprgOLD  4919  uniintsn  4982  uniop  5506  unex  7727  nlim2  8486  rankxplim  9871  mrcun  17571  indistps  22858  indistps2  22859  leordtval2  23060  ex-uni  30173  mnuprdlem1  43580  mnuprdlem2  43581  mnurndlem1  43589  fouriersw  45492
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