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Theorem unisn0 45064
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 4005 . 2 {∅} ⊆ {∅}
2 uni0b 4932 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 231 1 {∅} = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wss 3950  c0 4332  {csn 4625   cuni 4906
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-11 2156  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ral 3061  df-rex 3070  df-v 3481  df-dif 3953  df-ss 3967  df-nul 4333  df-sn 4626  df-uni 4907
This theorem is referenced by:  founiiun0  45200  prsal  46338
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