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Theorem prnz 4149
 Description: A pair containing a set is not empty. (Contributed by NM, 9-Apr-1994.)
Hypothesis
Ref Expression
prnz.1
Assertion
Ref Expression
prnz

Proof of Theorem prnz
StepHypRef Expression
1 prnz.1 . . 3
21prid1 4138 . 2
32ne0ii 3791 1
 Colors of variables: wff setvar class Syntax hints:  e.wcel 1818  =/=wne 2652   cvv 3109   c0 3784  {cpr 4031 This theorem is referenced by:  prnzg  4150  opnz  4723  fiint  7817  wilthlem2  23343  edgwlk  24531  umgrabi  24983  shincli  26280  chincli  26378 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-un 3480  df-nul 3785  df-sn 4030  df-pr 4032
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