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Theorem inteximm 3991
Description: The intersection of an inhabited class exists. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
inteximm (∃𝑥 𝑥𝐴 𝐴 ∈ V)
Distinct variable group:   𝑥,𝐴

Proof of Theorem inteximm
StepHypRef Expression
1 intss1 3709 . . 3 (𝑥𝐴 𝐴𝑥)
2 vex 2623 . . . 4 𝑥 ∈ V
32ssex 3982 . . 3 ( 𝐴𝑥 𝐴 ∈ V)
41, 3syl 14 . 2 (𝑥𝐴 𝐴 ∈ V)
54exlimiv 1535 1 (∃𝑥 𝑥𝐴 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1427  wcel 1439  Vcvv 2620  wss 3000   cint 3694
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-in 3006  df-ss 3013  df-int 3695
This theorem is referenced by:  intexabim  3994  iinexgm  3996  onintonm  4347
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