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Mirrors > Home > MPE Home > Th. List > unrab | Structured version Visualization version Unicode version |
Description: Union of two restricted class abstractions. (Contributed by NM, 25-Mar-2004.) |
Ref | Expression |
---|---|
unrab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rab 2921 | . . 3 | |
2 | df-rab 2921 | . . 3 | |
3 | 1, 2 | uneq12i 3765 | . 2 |
4 | df-rab 2921 | . . 3 | |
5 | unab 3894 | . . . 4 | |
6 | andi 911 | . . . . 5 | |
7 | 6 | abbii 2739 | . . . 4 |
8 | 5, 7 | eqtr4i 2647 | . . 3 |
9 | 4, 8 | eqtr4i 2647 | . 2 |
10 | 3, 9 | eqtr4i 2647 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wo 383 wa 384 wceq 1483 wcel 1990 cab 2608 crab 2916 cun 3572 |
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-rab 2921 df-v 3202 df-un 3579 |
This theorem is referenced by: rabxm 3961 kmlem3 8974 hashbclem 13236 phiprmpw 15481 efgsfo 18152 dsmmacl 20085 rrxmvallem 23187 mumul 24907 ppiub 24929 lgsquadlem2 25106 edglnl 26038 numclwwlk3lem 27241 hasheuni 30147 measvuni 30277 aean 30307 subfacp1lem6 31167 lineunray 32254 cnambfre 33458 itg2addnclem2 33462 iblabsnclem 33473 orrabdioph 37345 undisjrab 38505 mndpsuppss 42152 |
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