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Mirrors > Home > MPE Home > Th. List > undir | Structured version Visualization version Unicode version |
Description: Distributive law for union over intersection. Theorem 29 of [Suppes] p. 27. (Contributed by NM, 30-Sep-2002.) |
Ref | Expression |
---|---|
undir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | undi 3874 | . 2 | |
2 | uncom 3757 | . 2 | |
3 | uncom 3757 | . . 3 | |
4 | uncom 3757 | . . 3 | |
5 | 3, 4 | ineq12i 3812 | . 2 |
6 | 1, 2, 5 | 3eqtr4i 2654 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 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-v 3202 df-un 3579 df-in 3581 |
This theorem is referenced by: undif1 4043 dfif4 4101 dfif5 4102 bwth 21213 |
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