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Theorem 0ov 6580
 Description: Operation value of the empty set. (Contributed by AV, 15-May-2021.)
Assertion
Ref Expression
0ov (𝐴𝐵) = ∅

Proof of Theorem 0ov
StepHypRef Expression
1 df-ov 6552 . 2 (𝐴𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2 0fv 6137 . 2 (∅‘⟨𝐴, 𝐵⟩) = ∅
31, 2eqtri 2632 1 (𝐴𝐵) = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ∅c0 3874  ⟨cop 4131  ‘cfv 5804  (class class class)co 6549 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-8 1979  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-nul 4717  ax-pow 4769 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-dm 5048  df-iota 5768  df-fv 5812  df-ov 6552 This theorem is referenced by:  2mpt20  6780  el2mpt2csbcl  7137  homarcl  16501  oppglsm  17880  mclsrcl  30712  iswwlksnon  41051  iswspthsnon  41052  wwlks2onv  41158
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