Theorem unisnOLD 4690

Description: Obsolete proof of unisn 4689 as of 16-Sep-2022. (Contributed by NM, 30-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Hypothesis

Ref	Expression
unisn.1	⊢ 𝐴 ∈ V

Assertion

Ref	Expression
unisnOLD	⊢ ∪ {𝐴} = 𝐴

Proof of Theorem unisnOLD

Step	Hyp	Ref	Expression
1		dfsn2 4411	. . 3 ⊢ {𝐴} = {𝐴, 𝐴}
2	1	unieqi 4682	. 2 ⊢ ∪ {𝐴} = ∪ {𝐴, 𝐴}
3		unisn.1	. . 3 ⊢ 𝐴 ∈ V
4	3, 3	unipr 4686	. 2 ⊢ ∪ {𝐴, 𝐴} = (𝐴 ∪ 𝐴)
5		unidm 3979	. 2 ⊢ (𝐴 ∪ 𝐴) = 𝐴
6	2, 4, 5	3eqtri 2806	1 ⊢ ∪ {𝐴} = 𝐴

Syntax hints:   = wceq 1601   ∈ wcel 2107  Vcvv 3398   ∪ cun 3790  {csn 4398  {cpr 4400  ∪ cuni 4673

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-ext 2754

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-rex 3096  df-v 3400  df-un 3797  df-sn 4399  df-pr 4401  df-uni 4674

This theorem is referenced by:  unisngOLD  4691