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Theorem prneli 3556
 Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, using . (Contributed by David A. Wheeler, 10-May-2015.)
Hypotheses
Ref Expression
prneli.1
prneli.2
Assertion
Ref Expression
prneli

Proof of Theorem prneli
StepHypRef Expression
1 prneli.1 . . 3
2 prneli.2 . . 3
31, 2nelpri 3555 . 2
43nelir 2407 1
 Colors of variables: wff set class Syntax hints:   wne 2309   wnel 2404  cpr 3532 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ne 2310  df-nel 2405  df-v 2691  df-un 3079  df-sn 3537  df-pr 3538 This theorem is referenced by: (None)
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