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Theorem nelprd 4051
 Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, deduction version. (Contributed by Alexander van der Vekens, 25-Jan-2018.)
Hypotheses
Ref Expression
nelprd.1
nelprd.2
Assertion
Ref Expression
nelprd

Proof of Theorem nelprd
StepHypRef Expression
1 nelprd.1 . 2
2 nelprd.2 . 2
3 neanior 2782 . . 3
4 elpri 4049 . . . 4
54con3i 135 . . 3
63, 5sylbi 195 . 2
71, 2, 6syl2anc 661 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  \/wo 368  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  {cpr 4031 This theorem is referenced by:  renfdisj  9668  pmtrprfv3  16479  perfectlem2  23505  usgra2pthlem1  32353 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-un 3480  df-sn 4030  df-pr 4032
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