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Mirrors > Home > ILE Home > Th. List > csbdmg | Unicode version |
Description: Distribute proper substitution through the domain of a class. (Contributed by Jim Kingdon, 8-Dec-2018.) |
Ref | Expression |
---|---|
csbdmg |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabg 3061 | . . 3 | |
2 | sbcex2 2962 | . . . . 5 | |
3 | sbcel2g 3023 | . . . . . 6 | |
4 | 3 | exbidv 1797 | . . . . 5 |
5 | 2, 4 | syl5bb 191 | . . . 4 |
6 | 5 | abbidv 2257 | . . 3 |
7 | 1, 6 | eqtrd 2172 | . 2 |
8 | dfdm3 4726 | . . 3 | |
9 | 8 | csbeq2i 3029 | . 2 |
10 | dfdm3 4726 | . 2 | |
11 | 7, 9, 10 | 3eqtr4g 2197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 wex 1468 wcel 1480 cab 2125 wsbc 2909 csb 3003 cop 3530 cdm 4539 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sbc 2910 df-csb 3004 df-br 3930 df-dm 4549 |
This theorem is referenced by: sbcfng 5270 |
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