![]() |
Mathbox for Glauco Siliprandi |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > unisn0 | Structured version Visualization version GIF version |
Description: The union of the singleton of the empty set is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020.) |
Ref | Expression |
---|---|
unisn0 | ⊢ ∪ {∅} = ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 4018 | . 2 ⊢ {∅} ⊆ {∅} | |
2 | uni0b 4938 | . 2 ⊢ (∪ {∅} = ∅ ↔ {∅} ⊆ {∅}) | |
3 | 1, 2 | mpbir 231 | 1 ⊢ ∪ {∅} = ∅ |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 ⊆ wss 3963 ∅c0 4339 {csn 4631 ∪ cuni 4912 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-11 2155 ax-ext 2706 |
This theorem depends on definitions: df-bi 207 df-an 396 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-ral 3060 df-rex 3069 df-v 3480 df-dif 3966 df-ss 3980 df-nul 4340 df-sn 4632 df-uni 4913 |
This theorem is referenced by: founiiun0 45133 prsal 46274 |
Copyright terms: Public domain | W3C validator |