Theorem 0ov 7404

Description: Operation value of the empty set. (Contributed by AV, 15-May-2021.)

Assertion

Ref	Expression
0ov	⊢ (𝐴∅𝐵) = ∅

Proof of Theorem 0ov

Step	Hyp	Ref	Expression
1		df-ov 7370	. 2 ⊢ (𝐴∅𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2		0fv 6881	. 2 ⊢ (∅‘⟨𝐴, 𝐵⟩) = ∅
3	1, 2	eqtri 2759	1 ⊢ (𝐴∅𝐵) = ∅

Syntax hints:   = wceq 1542  ∅c0 4273  ⟨cop 4573  ‘cfv 6498  (class class class)co 7367

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708  ax-nul 5241  ax-pr 5375

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-mo 2539  df-eu 2569  df-clab 2715  df-cleq 2728  df-clel 2811  df-ne 2933  df-rab 3390  df-v 3431  df-dif 3892  df-un 3894  df-ss 3906  df-nul 4274  df-if 4467  df-sn 4568  df-pr 4570  df-op 4574  df-uni 4851  df-br 5086  df-dm 5641  df-iota 6454  df-fv 6506  df-ov 7370

This theorem is referenced by:  csbov  7412  2mpo0  7616  el2mpocsbcl  8035  homarcl  17995  oppglsm  19617  iswwlksnon  29921  iswspthsnon  29924  mclsrcl  35743  oppcup3  49684  indthinc  49937  indthincALT  49938  prsthinc  49939  lanrcl  50096  ranrcl  50097  rellan  50098  relran  50099