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Theorem prneli 4150
 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 𝐴𝐵
prneli.2 𝐴𝐶
Assertion
Ref Expression
prneli 𝐴 ∉ {𝐵, 𝐶}

Proof of Theorem prneli
StepHypRef Expression
1 prneli.1 . . 3 𝐴𝐵
2 prneli.2 . . 3 𝐴𝐶
31, 2nelpri 4149 . 2 ¬ 𝐴 ∈ {𝐵, 𝐶}
43nelir 2886 1 𝐴 ∉ {𝐵, 𝐶}
 Colors of variables: wff setvar class Syntax hints:   ≠ wne 2780   ∉ wnel 2781  {cpr 4127 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ne 2782  df-nel 2783  df-v 3175  df-un 3545  df-sn 4126  df-pr 4128 This theorem is referenced by:  vdegp1ai-av  40752
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