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Theorem nelpri 3979
 Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair. (Contributed by David A. Wheeler, 10-May-2015.)
Hypotheses
Ref Expression
nelpri.1
nelpri.2
Assertion
Ref Expression
nelpri

Proof of Theorem nelpri
StepHypRef Expression
1 nelpri.1 . 2
2 nelpri.2 . 2
3 neanior 2735 . . 3
4 elpri 3976 . . . 4
54con3i 142 . . 3
63, 5sylbi 200 . 2
71, 2, 6mp2an 686 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 375   wa 376   wceq 1452   wcel 1904   wne 2641  cpr 3961 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-v 3033  df-un 3395  df-sn 3960  df-pr 3962 This theorem is referenced by:  prneli  3980  constr3pthlem1  25462  konigsberg  25794  ex-dif  25952  ex-in  25954  ex-pss  25957  ex-res  25970
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