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Theorem inteximm 4239
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 3943 . . 3 (𝑥𝐴 𝐴𝑥)
2 vex 2805 . . . 4 𝑥 ∈ V
32ssex 4226 . . 3 ( 𝐴𝑥 𝐴 ∈ V)
41, 3syl 14 . 2 (𝑥𝐴 𝐴 ∈ V)
54exlimiv 1646 1 (∃𝑥 𝑥𝐴 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1540  wcel 2202  Vcvv 2802  wss 3200   cint 3928
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-sep 4207
This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-in 3206  df-ss 3213  df-int 3929
This theorem is referenced by:  intexabim  4242  iinexgm  4244  onintonm  4615  elfi2  7171  elfir  7172  fifo  7179
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