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Theorem unisn0 44994
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 4018 . 2 {∅} ⊆ {∅}
2 uni0b 4938 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 231 1 {∅} = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1537  wss 3963  c0 4339  {csn 4631   cuni 4912
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-11 2155  ax-ext 2706
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ral 3060  df-rex 3069  df-v 3480  df-dif 3966  df-ss 3980  df-nul 4340  df-sn 4632  df-uni 4913
This theorem is referenced by:  founiiun0  45133  prsal  46274
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