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Theorem 0ov 7192
 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 7158 . 2 (𝐴𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2 0fv 6708 . 2 (∅‘⟨𝐴, 𝐵⟩) = ∅
31, 2eqtri 2844 1 (𝐴𝐵) = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1533  ∅c0 4290  ⟨cop 4572  ‘cfv 6354  (class class class)co 7155 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907  ax-6 1966  ax-7 2011  ax-8 2112  ax-9 2120  ax-10 2141  ax-11 2157  ax-12 2173  ax-ext 2793  ax-nul 5209  ax-pow 5265 This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1536  df-ex 1777  df-nf 1781  df-sb 2066  df-mo 2618  df-eu 2650  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ral 3143  df-rex 3144  df-rab 3147  df-v 3496  df-dif 3938  df-un 3940  df-in 3942  df-ss 3951  df-nul 4291  df-if 4467  df-sn 4567  df-pr 4569  df-op 4573  df-uni 4838  df-br 5066  df-dm 5564  df-iota 6313  df-fv 6362  df-ov 7158 This theorem is referenced by:  csbov  7198  2mpo0  7393  el2mpocsbcl  7779  homarcl  17287  oppglsm  18766  iswwlksnon  27630  iswspthsnon  27633  mclsrcl  32808
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