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Theorem unisngOLD 4675
 Description: Obsolete proof of unisng 4672 as of 16-Sep-2022. (Contributed by NM, 13-Aug-2002.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
unisngOLD (𝐴𝑉 {𝐴} = 𝐴)

Proof of Theorem unisngOLD
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 sneq 4406 . . . 4 (𝑥 = 𝐴 → {𝑥} = {𝐴})
21unieqd 4667 . . 3 (𝑥 = 𝐴 {𝑥} = {𝐴})
3 id 22 . . 3 (𝑥 = 𝐴𝑥 = 𝐴)
42, 3eqeq12d 2839 . 2 (𝑥 = 𝐴 → ( {𝑥} = 𝑥 {𝐴} = 𝐴))
5 vex 3416 . . 3 𝑥 ∈ V
65unisnOLD 4674 . 2 {𝑥} = 𝑥
74, 6vtoclg 3481 1 (𝐴𝑉 {𝐴} = 𝐴)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   = wceq 1658   ∈ wcel 2166  {csn 4396  ∪ cuni 4657 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-ext 2802 This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2811  df-cleq 2817  df-clel 2820  df-nfc 2957  df-rex 3122  df-v 3415  df-un 3802  df-sn 4397  df-pr 4399  df-uni 4658 This theorem is referenced by: (None)
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