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Mirrors > Home > ILE Home > Th. List > csbresg | Unicode version |
Description: Distribute proper substitution through the restriction of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbresg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbing 3144 | . . 3 | |
2 | csbxpg 4421 | . . . . 5 | |
3 | csbconstg 2864 | . . . . . 6 | |
4 | 3 | xpeq2d 4369 | . . . . 5 |
5 | 2, 4 | eqtrd 2072 | . . . 4 |
6 | 5 | ineq2d 3138 | . . 3 |
7 | 1, 6 | eqtrd 2072 | . 2 |
8 | df-res 4357 | . . 3 | |
9 | 8 | csbeq2i 2876 | . 2 |
10 | df-res 4357 | . 2 | |
11 | 7, 9, 10 | 3eqtr4g 2097 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1243 wcel 1393 cvv 2557 csb 2852 cin 2916 cxp 4343 cres 4347 |
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-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rab 2315 df-v 2559 df-sbc 2765 df-csb 2853 df-in 2924 df-opab 3819 df-xp 4351 df-res 4357 |
This theorem is referenced by: (None) |
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