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| Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. |
| Ref | Expression |
|---|---|
| intun |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 19.26 1732 |
. . . 4
| |
| 2 | elun 2992 |
. . . . . . 7
| |
| 3 | 2 | imbi1i 375 |
. . . . . 6
|
| 4 | jaob 879 |
. . . . . 6
| |
| 5 | 3, 4 | bitri 306 |
. . . . 5
|
| 6 | 5 | albii 1664 |
. . . 4
|
| 7 | visset 2572 |
. . . . . 6
| |
| 8 | 7 | elint 3438 |
. . . . 5
|
| 9 | 7 | elint 3438 |
. . . . 5
|
| 10 | 8, 9 | anbi12i 806 |
. . . 4
|
| 11 | 1, 6, 10 | 3bitr4i 340 |
. . 3
|
| 12 | 7 | elint 3438 |
. . 3
|
| 13 | elin 3031 |
. . 3
| |
| 14 | 11, 12, 13 | 3bitr4i 340 |
. 2
|
| 15 | 14 | eqriv 2167 |
1
|
| Colors of variables: wff set class |
| Syntax hints: |
| This theorem is referenced by: intunsn 3467 abfii4 5920 subbas 9915 fbssint 11275 infi 11276 fbunfip 11278 infi1 15312 moec 15320 ficli 15324 elfiun 16454 fcluscomplem 16705 |
| This theorem was proved from axioms: ax-1 4 ax-2 5 ax-3 6 ax-mp 7 ax-7 1621 ax-gen 1622 ax-8 1623 ax-9 1624 ax-10 1625 ax-11 1626 ax-12 1627 ax-17 1634 ax-4 1637 ax-5o 1639 ax-6o 1642 ax-9o 1792 ax-10o 1810 ax-16 1883 ax-11o 1893 ax-ext 2152 |
| This theorem depends on definitions: df-bi 232 df-or 434 df-an 435 df-ex 1645 df-sb 1845 df-clab 2158 df-cleq 2163 df-clel 2166 df-v 2571 df-un 2864 df-in 2866 df-int 3433 |