Theorem uni0OLD 4890

Description: Obsolete version of uni0 4889 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5249. (Revised by Eric Schmidt, 4-Apr-2007.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
uni0OLD	⊢ ∪ ∅ = ∅

Proof of Theorem uni0OLD

Step	Hyp	Ref	Expression
1		0ss 4350	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4887	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 231	1 ⊢ ∪ ∅ = ∅

Syntax hints:   = wceq 1541   ⊆ wss 3899  ∅c0 4283  {csn 4578  ∪ cuni 4861

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-11 2162  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-ral 3050  df-rex 3059  df-v 3440  df-dif 3902  df-ss 3916  df-nul 4284  df-sn 4579  df-uni 4862

This theorem is referenced by: (None)