Theorem uni0OLD 4879

Description: Obsolete version of uni0 4878 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5241. (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 4340	. 2 ⊢ ∅ ⊆ {∅}
2		uni0b 4876	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 231	1 ⊢ ∪ ∅ = ∅

Syntax hints:   = wceq 1542   ⊆ wss 3889  ∅c0 4273  {csn 4567  ∪ cuni 4850

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-11 2163  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-ral 3052  df-rex 3062  df-v 3431  df-dif 3892  df-ss 3906  df-nul 4274  df-sn 4568  df-uni 4851

This theorem is referenced by: (None)