Mathbox for Glauco Siliprandi < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  unisn0 Structured version   Visualization version   GIF version

Theorem unisn0 40876
 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 3916 . 2 {∅} ⊆ {∅}
2 uni0b 4776 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 232 1 {∅} = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1525   ⊆ wss 3865  ∅c0 4217  {csn 4478  ∪ cuni 4751 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1781  ax-4 1795  ax-5 1892  ax-6 1951  ax-7 1996  ax-8 2085  ax-9 2093  ax-10 2114  ax-11 2128  ax-12 2143  ax-ext 2771 This theorem depends on definitions:  df-bi 208  df-an 397  df-or 843  df-tru 1528  df-ex 1766  df-nf 1770  df-sb 2045  df-clab 2778  df-cleq 2790  df-clel 2865  df-nfc 2937  df-ral 3112  df-rex 3113  df-v 3442  df-dif 3868  df-in 3872  df-ss 3880  df-nul 4218  df-sn 4479  df-uni 4752 This theorem is referenced by:  founiiun0  41012  prsal  42167
 Copyright terms: Public domain W3C validator