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Theorem opnssborel 42413
Description: Open sets of a generalized real Euclidean space are Borel sets (notice that this theorem is even more general, because 𝑋 is not required to be a set). (Contributed by Glauco Siliprandi, 3-Jan-2021.)
Hypotheses
Ref Expression
opnssborel.a 𝐴 = (TopOpen‘(ℝ^‘𝑋))
opnssborel.b 𝐵 = (SalGen‘𝐴)
Assertion
Ref Expression
opnssborel 𝐴𝐵

Proof of Theorem opnssborel
StepHypRef Expression
1 opnssborel.a . . 3 𝐴 = (TopOpen‘(ℝ^‘𝑋))
21fvexi 6544 . 2 𝐴 ∈ V
3 opnssborel.b . . 3 𝐵 = (SalGen‘𝐴)
43sssalgen 42114 . 2 (𝐴 ∈ V → 𝐴𝐵)
52, 4ax-mp 5 1 𝐴𝐵
Colors of variables: wff setvar class
Syntax hints:   = wceq 1520  wcel 2079  Vcvv 3432  wss 3854  cfv 6217  TopOpenctopn 16512  ℝ^crrx 23657  SalGencsalgen 42093
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1775  ax-4 1789  ax-5 1886  ax-6 1945  ax-7 1990  ax-8 2081  ax-9 2089  ax-10 2110  ax-11 2124  ax-12 2139  ax-13 2342  ax-ext 2767  ax-sep 5088  ax-nul 5095  ax-pow 5150  ax-pr 5214  ax-un 7310
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-3an 1080  df-tru 1523  df-ex 1760  df-nf 1764  df-sb 2041  df-mo 2574  df-eu 2610  df-clab 2774  df-cleq 2786  df-clel 2861  df-nfc 2933  df-ne 2983  df-ral 3108  df-rex 3109  df-rab 3112  df-v 3434  df-sbc 3702  df-csb 3807  df-dif 3857  df-un 3859  df-in 3861  df-ss 3869  df-nul 4207  df-if 4376  df-pw 4449  df-sn 4467  df-pr 4469  df-op 4473  df-uni 4740  df-int 4777  df-br 4957  df-opab 5019  df-mpt 5036  df-id 5340  df-xp 5441  df-rel 5442  df-cnv 5443  df-co 5444  df-dm 5445  df-iota 6181  df-fun 6219  df-fv 6225  df-salg 42090  df-salgen 42094
This theorem is referenced by: (None)
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