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

Theorem unisn0 38744
 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 3609 . 2 {∅} ⊆ {∅}
2 uni0b 4436 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 221 1 {∅} = ∅
 Colors of variables: wff setvar class Syntax hints:   = wceq 1480   ⊆ wss 3560  ∅c0 3897  {csn 4155  ∪ cuni 4409 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601 This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-ral 2913  df-rex 2914  df-v 3192  df-dif 3563  df-in 3567  df-ss 3574  df-nul 3898  df-sn 4156  df-uni 4410 This theorem is referenced by:  founiiun0  38886
 Copyright terms: Public domain W3C validator