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Theorem unisn0 41196
Description: The union of the singleton of the empty set is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020.)
Assertion
Ref Expression
unisn0 {∅} = ∅

Proof of Theorem unisn0
StepHypRef Expression
1 ssid 3988 . 2 {∅} ⊆ {∅}
2 uni0b 4857 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 232 1 {∅} = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  wss 3935  c0 4290  {csn 4559   cuni 4832
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2151  ax-12 2167  ax-ext 2793
This theorem depends on definitions:  df-bi 208  df-an 397  df-or 842  df-tru 1531  df-ex 1772  df-nf 1776  df-sb 2061  df-clab 2800  df-cleq 2814  df-clel 2893  df-nfc 2963  df-ral 3143  df-rex 3144  df-v 3497  df-dif 3938  df-in 3942  df-ss 3951  df-nul 4291  df-sn 4560  df-uni 4833
This theorem is referenced by:  founiiun0  41331  prsal  42484
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