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Theorem unisn0 42061
 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 3914 . 2 {∅} ⊆ {∅}
2 uni0b 4826 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 234 1 {∅} = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ⊆ wss 3858  ∅c0 4225  {csn 4522  ∪ cuni 4798 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-11 2158  ax-ext 2729 This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1541  df-fal 1551  df-ex 1782  df-sb 2070  df-clab 2736  df-cleq 2750  df-clel 2830  df-ral 3075  df-rex 3076  df-v 3411  df-dif 3861  df-in 3865  df-ss 3875  df-nul 4226  df-sn 4523  df-uni 4799 This theorem is referenced by:  founiiun0  42187  prsal  43326
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