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Mirrors > Home > NFE Home > Th. List > resundir | Unicode version |
Description: Distributive law for restriction over union. (Contributed by set.mm contributors, 23-Sep-2004.) |
Ref | Expression |
---|---|
resundir |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | indir 3503 | . 2 | |
2 | df-res 4788 | . 2 | |
3 | df-res 4788 | . . 3 | |
4 | df-res 4788 | . . 3 | |
5 | 3, 4 | uneq12i 3416 | . 2 |
6 | 1, 2, 5 | 3eqtr4i 2383 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 cvv 2859 cun 3207 cin 3208 cxp 4770 cres 4774 |
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 df-res 4788 |
This theorem is referenced by: imaundir 5040 fvunsn 5444 fvsnun1 5447 fvsnun2 5448 |
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