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Mirrors > Home > MPE Home > Th. List > ex-uni | Structured version Visualization version GIF version |
Description: Example for df-uni 4820. 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 5325 | . . 3 ⊢ {1, 3} ∈ V | |
2 | prex 5325 | . . 3 ⊢ {1, 8} ∈ V | |
3 | 1, 2 | unipr 4837 | . 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8}) |
4 | ex-un 28507 | . 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 1543 ∪ cun 3864 {cpr 4543 {ctp 4545 ∪ cuni 4819 1c1 10730 3c3 11886 8c8 11891 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1803 ax-4 1817 ax-5 1918 ax-6 1976 ax-7 2016 ax-8 2112 ax-9 2120 ax-ext 2708 ax-sep 5192 ax-nul 5199 ax-pr 5322 |
This theorem depends on definitions: df-bi 210 df-an 400 df-or 848 df-tru 1546 df-fal 1556 df-ex 1788 df-sb 2071 df-clab 2715 df-cleq 2729 df-clel 2816 df-v 3410 df-dif 3869 df-un 3871 df-in 3873 df-ss 3883 df-nul 4238 df-sn 4542 df-pr 4544 df-tp 4546 df-uni 4820 |
This theorem is referenced by: (None) |
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