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Mirrors > Home > MPE Home > Th. List > ex-uni | Structured version Visualization version GIF version |
Description: Example for df-uni 4373. 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 4836 | . . 3 ⊢ {1, 3} ∈ V | |
2 | prex 4836 | . . 3 ⊢ {1, 8} ∈ V | |
3 | 1, 2 | unipr 4385 | . 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8}) |
4 | ex-un 26673 | . 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8} | |
5 | 3, 4 | eqtri 2632 | 1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8} |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ∪ cun 3538 {cpr 4127 {ctp 4129 ∪ cuni 4372 1c1 9816 3c3 10948 8c8 10953 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-9 1986 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 ax-sep 4709 ax-nul 4717 ax-pr 4833 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-v 3175 df-dif 3543 df-un 3545 df-in 3547 df-ss 3554 df-nul 3875 df-sn 4126 df-pr 4128 df-tp 4130 df-uni 4373 |
This theorem is referenced by: (None) |
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