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Mirrors > Home > MPE Home > Th. List > difindi | Structured version Visualization version Unicode version |
Description: Distributive law for class difference. Theorem 40 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.) |
Ref | Expression |
---|---|
difindi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfin3 3866 | . . 3 | |
2 | 1 | difeq2i 3725 | . 2 |
3 | indi 3873 | . . 3 | |
4 | dfin2 3860 | . . 3 | |
5 | invdif 3868 | . . . 4 | |
6 | invdif 3868 | . . . 4 | |
7 | 5, 6 | uneq12i 3765 | . . 3 |
8 | 3, 4, 7 | 3eqtr3i 2652 | . 2 |
9 | 2, 8 | eqtri 2644 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cvv 3200 cdif 3571 cun 3572 cin 3573 |
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-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 |
This theorem is referenced by: difdif2 3884 indm 3886 fndifnfp 6442 dprddisj2 18438 fctop 20808 cctop 20810 mretopd 20896 restcld 20976 cfinfil 21697 csdfil 21698 indifundif 29356 difres 29413 unelcarsg 30374 clsk3nimkb 38338 ntrclskb 38367 ntrclsk3 38368 ntrclsk13 38369 salincl 40543 |
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