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Theorem 0ov 6667
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 6638 . 2 (𝐴𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2 0fv 6214 . 2 (∅‘⟨𝐴, 𝐵⟩) = ∅
31, 2eqtri 2642 1 (𝐴𝐵) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  c0 3907  cop 4174  cfv 5876  (class class class)co 6635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-8 1990  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-nul 4780  ax-pow 4834
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-mo 2473  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ral 2914  df-rex 2915  df-rab 2918  df-v 3197  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-if 4078  df-sn 4169  df-pr 4171  df-op 4175  df-uni 4428  df-br 4645  df-dm 5114  df-iota 5839  df-fv 5884  df-ov 6638
This theorem is referenced by:  2mpt20  6867  el2mpt2csbcl  7235  homarcl  16659  oppglsm  18038  iswwlksnon  26721  iswspthsnon  26722  wwlks2onv  26828  mclsrcl  31432
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