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Theorem nelpri 3695
 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 2564 . . 3
4 elpri 3694 . . . 4
54con3i 127 . . 3
63, 5sylbi 187 . 2
71, 2, 6mp2an 653 1
 Colors of variables: wff set class Syntax hints:   wn 3   wo 357   wa 358   wceq 1633   wcel 1701   wne 2479  cpr 3675 This theorem is referenced by:  ex-dif  20863  ex-in  20865  ex-pss  20868  ex-res  20881  konigsberg  24195  ftp  26041  constr3pthlem1  27539  AnelBC  27683 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-v 2824  df-un 3191  df-sn 3680  df-pr 3681
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