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Mirrors > Home > NFE Home > Th. List > dfun4 | Unicode version |
Description: Definition of union in terms of intersection. (Contributed by SF, 12-Jan-2015.) |
Ref | Expression |
---|---|
dfun4 | ∼ ∼ ∼ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfin5 3545 | . . 3 ∼ ∼ ∼ ∼ ∼ ∼ ∼ | |
2 | 1 | compleqi 3244 | . 2 ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ |
3 | dblcompl 3227 | . 2 ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ ∼ | |
4 | dblcompl 3227 | . . 3 ∼ ∼ | |
5 | dblcompl 3227 | . . 3 ∼ ∼ | |
6 | 4, 5 | uneq12i 3416 | . 2 ∼ ∼ ∼ ∼ |
7 | 2, 3, 6 | 3eqtrri 2378 | 1 ∼ ∼ ∼ |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 ∼ ccompl 3205 cun 3207 cin 3208 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 |
This theorem is referenced by: iinun 3548 |
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