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Theorem unisn0 39743
 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 3773 . 2 {∅} ⊆ {∅}
2 uni0b 4600 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 221 1 {∅} = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1631   ⊆ wss 3723  ∅c0 4063  {csn 4317  ∪ cuni 4575 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1870  ax-4 1885  ax-5 1991  ax-6 2057  ax-7 2093  ax-9 2154  ax-10 2174  ax-11 2190  ax-12 2203  ax-13 2408  ax-ext 2751 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-tru 1634  df-ex 1853  df-nf 1858  df-sb 2050  df-clab 2758  df-cleq 2764  df-clel 2767  df-nfc 2902  df-ral 3066  df-rex 3067  df-v 3353  df-dif 3726  df-in 3730  df-ss 3737  df-nul 4064  df-sn 4318  df-uni 4576 This theorem is referenced by:  founiiun0  39896
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