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Theorem 0ov 6722
 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 6693 . 2 (𝐴𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2 0fv 6265 . 2 (∅‘⟨𝐴, 𝐵⟩) = ∅
31, 2eqtri 2673 1 (𝐴𝐵) = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1523  ∅c0 3948  ⟨cop 4216  ‘cfv 5926  (class class class)co 6690 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-8 2032  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-nul 4822  ax-pow 4873 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-ral 2946  df-rex 2947  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-uni 4469  df-br 4686  df-dm 5153  df-iota 5889  df-fv 5934  df-ov 6693 This theorem is referenced by:  2mpt20  6924  el2mpt2csbcl  7295  homarcl  16725  oppglsm  18103  iswwlksnon  26802  iswwlksnonOLD  26803  iswspthsnon  26806  iswspthsnonOLD  26807  mclsrcl  31584
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