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Theorem unisn0 42491
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 3939 . 2 {∅} ⊆ {∅}
2 uni0b 4864 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 230 1 {∅} = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wss 3883  c0 4253  {csn 4558   cuni 4836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-11 2156  ax-ext 2709
This theorem depends on definitions:  df-bi 206  df-an 396  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-ral 3068  df-rex 3069  df-v 3424  df-dif 3886  df-in 3890  df-ss 3900  df-nul 4254  df-sn 4559  df-uni 4837
This theorem is referenced by:  founiiun0  42617  prsal  43749
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