![]() |
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 4871. 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 5394 | . . 3 ⊢ {1, 3} ∈ V | |
2 | prex 5394 | . . 3 ⊢ {1, 8} ∈ V | |
3 | 1, 2 | unipr 4888 | . 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8}) |
4 | ex-un 29410 | . 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8} | |
5 | 3, 4 | eqtri 2765 | 1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ∪ cun 3913 {cpr 4593 {ctp 4595 ∪ cuni 4870 1c1 11059 3c3 12216 8c8 12221 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2708 ax-sep 5261 ax-nul 5268 ax-pr 5389 |
This theorem depends on definitions: df-bi 206 df-an 398 df-or 847 df-tru 1545 df-fal 1555 df-ex 1783 df-sb 2069 df-clab 2715 df-cleq 2729 df-clel 2815 df-v 3450 df-dif 3918 df-un 3920 df-in 3922 df-ss 3932 df-nul 4288 df-sn 4592 df-pr 4594 df-tp 4596 df-uni 4871 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |