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Theorem inteximm 3903
 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 3630 . . 3 (𝑥𝐴 𝐴𝑥)
2 vex 2560 . . . 4 𝑥 ∈ V
32ssex 3894 . . 3 ( 𝐴𝑥 𝐴 ∈ V)
41, 3syl 14 . 2 (𝑥𝐴 𝐴 ∈ V)
54exlimiv 1489 1 (∃𝑥 𝑥𝐴 𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4  ∃wex 1381   ∈ wcel 1393  Vcvv 2557   ⊆ wss 2917  ∩ cint 3615 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-int 3616 This theorem is referenced by:  intexabim  3906  iinexgm  3908  onintonm  4243
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