Theorem uni0OLD 4897

Description: Obsolete version of uni0 4896 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5258. (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 4356	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4894	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 233	1 ⊢ ∪ ∅ = ∅

Syntax hints:   = wceq 1562   ⊆ wss 3906  ∅c0 4287  {csn 4584  ∪ cuni 4867

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1817  ax-4 1831  ax-5 1932  ax-6 1989  ax-7 2030  ax-8 2146  ax-9 2154  ax-11 2193  ax-ext 2736

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1565  df-fal 1575  df-ex 1802  df-sb 2093  df-clab 2743  df-cleq 2756  df-clel 2839  df-ral 3079  df-rex 3089  df-v 3458  df-dif 3909  df-ss 3923  df-nul 4288  df-sn 4585  df-uni 4868

This theorem is referenced by: (None)