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Theorem prmg 3489
 Description: A pair containing a set is inhabited. (Contributed by Jim Kingdon, 21-Sep-2018.)
Assertion
Ref Expression
prmg
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem prmg
StepHypRef Expression
1 snmg 3486 . 2
2 orc 633 . . . 4
3 velsn 3392 . . . 4
4 vex 2560 . . . . 5
54elpr 3396 . . . 4
62, 3, 53imtr4i 190 . . 3
76eximi 1491 . 2
81, 7syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wo 629   wceq 1243  wex 1381   wcel 1393  csn 3375  cpr 3376 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 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-un 2922  df-sn 3381  df-pr 3382 This theorem is referenced by:  prm  3491  opm  3971  onintexmid  4297
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