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Mirrors > Home > MPE Home > Th. List > intun | Structured version Visualization version Unicode version |
Description: The class intersection of the union of two classes. Theorem 78 of [Suppes] p. 42. (Contributed by NM, 22-Sep-2002.) |
Ref | Expression |
---|---|
intun |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1798 | . . . 4 | |
2 | elun 3753 | . . . . . . 7 | |
3 | 2 | imbi1i 339 | . . . . . 6 |
4 | jaob 822 | . . . . . 6 | |
5 | 3, 4 | bitri 264 | . . . . 5 |
6 | 5 | albii 1747 | . . . 4 |
7 | vex 3203 | . . . . . 6 | |
8 | 7 | elint 4481 | . . . . 5 |
9 | 7 | elint 4481 | . . . . 5 |
10 | 8, 9 | anbi12i 733 | . . . 4 |
11 | 1, 6, 10 | 3bitr4i 292 | . . 3 |
12 | 7 | elint 4481 | . . 3 |
13 | elin 3796 | . . 3 | |
14 | 11, 12, 13 | 3bitr4i 292 | . 2 |
15 | 14 | eqriv 2619 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wo 383 wa 384 wal 1481 wceq 1483 wcel 1990 cun 3572 cin 3573 cint 4475 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-v 3202 df-un 3579 df-in 3581 df-int 4476 |
This theorem is referenced by: intunsn 4516 riinint 5382 fiin 8328 elfiun 8336 elrfi 37257 |
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