Theorem uni0OLD 4901

Description: Obsolete version of uni0 4900 as of 1-Feb-2026. (Contributed by NM, 16-Sep-1993.) Remove use of ax-nul 5268. (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 4898	. 2 ⊢ (∪ ∅ = ∅ ↔ ∅ ⊆ {∅})
3	1, 2	mpbir 234	1 ⊢ ∪ ∅ = ∅

Syntax hints:   = wceq 1568   ⊆ wss 3904  ∅c0 4285  {csn 4588  ∪ cuni 4871

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1823  ax-4 1837  ax-5 1938  ax-6 1995  ax-7 2036  ax-8 2143  ax-9 2151  ax-11 2190  ax-ext 2733

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1571  df-fal 1581  df-ex 1808  df-sb 2095  df-clab 2740  df-cleq 2753  df-clel 2836  df-ral 3078  df-rex 3088  df-v 3455  df-dif 3907  df-ss 3921  df-nul 4286  df-sn 4589  df-uni 4872

This theorem is referenced by: (None)