Theorem uni0OLD 4870

Description: Obsolete version of uni0 4869 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5231. (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 4331	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4867	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 233	1 ⊢ ∪ ∅ = ∅

Syntax hints:   = wceq 1548   ⊆ wss 3885  ∅c0 4264  {csn 4558  ∪ cuni 4841

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1975  ax-7 2016  ax-8 2123  ax-9 2131  ax-11 2170  ax-ext 2713

This theorem depends on definitions:  df-bi 209  df-an 398  df-tru 1551  df-fal 1561  df-ex 1788  df-sb 2075  df-clab 2720  df-cleq 2733  df-clel 2816  df-ral 3056  df-rex 3066  df-v 3435  df-dif 3888  df-ss 3902  df-nul 4265  df-sn 4559  df-uni 4842

This theorem is referenced by: (None)