Theorem uni0OLD 4907

Description: Obsolete version of uni0 4906 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5274. (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 4360	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4904	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 234	1 ⊢ ∪ ∅ = ∅

This proof depends on syntax axioms:   = wceq 1570   ⊆ wss 3908  ∅c0 4289  {csn 4594  ∪ cuni 4877

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-11 2195  ax-ext 2738

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-ral 3083  df-rex 3093  df-v 3460  df-dif 3911  df-ss 3925  df-nul 4290  df-sn 4595  df-uni 4878

This theorem is used by: (None)