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

Theorem unisn0 39981
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 3819 . 2 {∅} ⊆ {∅}
2 uni0b 4655 . 2 ( {∅} = ∅ ↔ {∅} ⊆ {∅})
31, 2mpbir 223 1 {∅} = ∅
Colors of variables: wff setvar class
Syntax hints:   = wceq 1653  wss 3769  c0 4115  {csn 4368   cuni 4628
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107  ax-9 2166  ax-10 2185  ax-11 2200  ax-12 2213  ax-13 2377  ax-ext 2777
This theorem depends on definitions:  df-bi 199  df-an 386  df-or 875  df-tru 1657  df-ex 1876  df-nf 1880  df-sb 2065  df-clab 2786  df-cleq 2792  df-clel 2795  df-nfc 2930  df-ral 3094  df-rex 3095  df-v 3387  df-dif 3772  df-in 3776  df-ss 3783  df-nul 4116  df-sn 4369  df-uni 4629
This theorem is referenced by:  founiiun0  40131
  Copyright terms: Public domain W3C validator