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Mirrors > Home > ILE Home > Th. List > csbsng | Unicode version |
Description: Distribute proper substitution through the singleton of a class. (Contributed by Alan Sare, 10-Nov-2012.) |
Ref | Expression |
---|---|
csbsng |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbabg 2963 | . . 3 | |
2 | sbceq2g 2928 | . . . 4 | |
3 | 2 | abbidv 2196 | . . 3 |
4 | 1, 3 | eqtrd 2113 | . 2 |
5 | df-sn 3404 | . . 3 | |
6 | 5 | csbeq2i 2932 | . 2 |
7 | df-sn 3404 | . 2 | |
8 | 4, 6, 7 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 cab 2067 wsbc 2815 csb 2908 csn 3398 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-sbc 2816 df-csb 2909 df-sn 3404 |
This theorem is referenced by: (None) |
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