Theorem uni0OLD 4900

Description: Obsolete version of uni0 4899 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5263. (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 4353	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4897	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 234	1 ⊢ ∪ ∅ = ∅

This proof depends on syntax axioms:   = wceq 1570   ⊆ wss 3900  ∅c0 4281  {csn 4588  ∪ cuni 4870

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-11 2197  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-ral 3081  df-rex 3091  df-v 3456  df-ss 3901  df-dif 4050  df-nul 4282  df-sn 4589  df-uni 4871

This theorem is used by: (None)