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Theorem inteximm 3894
Description: The intersection of an inhabited class exists. (Contributed by Jim Kingdon, 27-Aug-2018.)
Assertion
Ref Expression
inteximm (x x A A V)
Distinct variable group:   x,A

Proof of Theorem inteximm
StepHypRef Expression
1 intss1 3621 . . 3 (x A Ax)
2 vex 2554 . . . 4 x V
32ssex 3885 . . 3 ( Ax A V)
41, 3syl 14 . 2 (x A A V)
54exlimiv 1486 1 (x x A A V)
Colors of variables: wff set class
Syntax hints:  wi 4  wex 1378   wcel 1390  Vcvv 2551  wss 2911   cint 3606
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-sep 3866
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-int 3607
This theorem is referenced by:  intexabim  3897  iinexgm  3899
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