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Theorem unipr 4924
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 4923 . 2 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → {𝐴, 𝐵} = (𝐴𝐵))
41, 2, 3mp2an 692 1 {𝐴, 𝐵} = (𝐴𝐵)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1540  wcel 2108  Vcvv 3480  cun 3949  {cpr 4628   cuni 4907
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629  df-uni 4908
This theorem is referenced by:  uniintsn  4985  uniop  5520  unexOLD  7765  nlim2  8528  rankxplim  9919  mrcun  17665  indistps  23018  indistps2  23019  leordtval2  23220  ex-uni  30445  mnuprdlem1  44291  mnuprdlem2  44292  mnurndlem1  44300  fouriersw  46246
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