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Theorem prm 3482
 Description: A pair containing a set is inhabited. (Contributed by Jim Kingdon, 21-Sep-2018.)
Hypothesis
Ref Expression
prnz.1 A V
Assertion
Ref Expression
prm x x {A, B}
Distinct variable groups:   x,A   x,B

Proof of Theorem prm
StepHypRef Expression
1 prnz.1 . 2 A V
2 prmg 3480 . 2 (A V → x x {A, B})
31, 2ax-mp 7 1 x x {A, B}
 Colors of variables: wff set class Syntax hints:  ∃wex 1378   ∈ wcel 1390  Vcvv 2551  {cpr 3368 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-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 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-un 2916  df-sn 3373  df-pr 3374 This theorem is referenced by: (None)
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