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Theorem 0ov 7438
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 7404 . 2 (𝐴𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2 0fv 6925 . 2 (∅‘⟨𝐴, 𝐵⟩) = ∅
31, 2eqtri 2752 1 (𝐴𝐵) = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1533  c0 4314  cop 4626  cfv 6533  (class class class)co 7401
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-nul 5296  ax-pr 5417
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-eu 2555  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-uni 4900  df-br 5139  df-dm 5676  df-iota 6485  df-fv 6541  df-ov 7404
This theorem is referenced by:  csbov  7444  2mpo0  7648  el2mpocsbcl  8065  homarcl  17977  oppglsm  19547  iswwlksnon  29531  iswspthsnon  29534  mclsrcl  35007  indthinc  47826  indthincALT  47827  prsthinc  47828
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