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Theorem prneli 4621
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 4620 . 2 ¬ 𝐴 ∈ {𝐵, 𝐶}
43nelir 3053 1 𝐴 ∉ {𝐵, 𝐶}
Colors of variables: wff setvar class
Syntax hints:  wne 2944  wnel 3050  {cpr 4593
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-ne 2945  df-nel 3051  df-v 3450  df-un 3920  df-sn 4592  df-pr 4594
This theorem is referenced by:  vdegp1ai  28526
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