|   | Metamath Proof Explorer | < Previous  
      Next > Nearby theorems | |
| Mirrors > Home > MPE Home > Th. List > ex-uni | Structured version Visualization version GIF version | ||
| Description: Example for df-uni 4907. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.) | 
| Ref | Expression | 
|---|---|
| ex-uni | ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8} | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | prex 5436 | . . 3 ⊢ {1, 3} ∈ V | |
| 2 | prex 5436 | . . 3 ⊢ {1, 8} ∈ V | |
| 3 | 1, 2 | unipr 4923 | . 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8}) | 
| 4 | ex-un 30444 | . 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8} | |
| 5 | 3, 4 | eqtri 2764 | 1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8} | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1539 ∪ cun 3948 {cpr 4627 {ctp 4629 ∪ cuni 4906 1c1 11157 3c3 12323 8c8 12328 | 
| 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-ext 2707 ax-sep 5295 ax-nul 5305 ax-pr 5431 | 
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-tru 1542 df-fal 1552 df-ex 1779 df-sb 2064 df-clab 2714 df-cleq 2728 df-clel 2815 df-v 3481 df-dif 3953 df-un 3955 df-ss 3967 df-nul 4333 df-sn 4626 df-pr 4628 df-tp 4630 df-uni 4907 | 
| This theorem is referenced by: (None) | 
| Copyright terms: Public domain | W3C validator |