Theorem 0ov 7395

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 7361	. 2 ⊢ (𝐴∅𝐵) = (∅‘⟨𝐴, 𝐵⟩)
2		0fv 6875	. 2 ⊢ (∅‘⟨𝐴, 𝐵⟩) = ∅
3	1, 2	eqtri 2759	1 ⊢ (𝐴∅𝐵) = ∅

Syntax hints:   = wceq 1541  ∅c0 4285  ⟨cop 4586  ‘cfv 6492  (class class class)co 7358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708  ax-nul 5251  ax-pr 5377

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-mo 2539  df-eu 2569  df-clab 2715  df-cleq 2728  df-clel 2811  df-ne 2933  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-uni 4864  df-br 5099  df-dm 5634  df-iota 6448  df-fv 6500  df-ov 7361

This theorem is referenced by:  csbov  7403  2mpo0  7607  el2mpocsbcl  8027  homarcl  17952  oppglsm  19571  iswwlksnon  29926  iswspthsnon  29929  mclsrcl  35755  oppcup3  49450  indthinc  49703  indthincALT  49704  prsthinc  49705  lanrcl  49862  ranrcl  49863  rellan  49864  relran  49865