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Mirrors > Home > ILE Home > Th. List > csbunig | Unicode version |
Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbunig |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabg 2907 | . . 3 | |
2 | sbcexg 2813 | . . . . 5 | |
3 | sbcang 2806 | . . . . . . 7 | |
4 | sbcg 2827 | . . . . . . . 8 | |
5 | sbcel2g 2871 | . . . . . . . 8 | |
6 | 4, 5 | anbi12d 442 | . . . . . . 7 |
7 | 3, 6 | bitrd 177 | . . . . . 6 |
8 | 7 | exbidv 1706 | . . . . 5 |
9 | 2, 8 | bitrd 177 | . . . 4 |
10 | 9 | abbidv 2155 | . . 3 |
11 | 1, 10 | eqtrd 2072 | . 2 |
12 | df-uni 3581 | . . 3 | |
13 | 12 | csbeq2i 2876 | . 2 |
14 | df-uni 3581 | . 2 | |
15 | 11, 13, 14 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wceq 1243 wex 1381 wcel 1393 cab 2026 wsbc 2764 csb 2852 cuni 3580 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-csb 2853 df-uni 3581 |
This theorem is referenced by: (None) |
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