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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 3110 | . . 3 | |
2 | sbceq2g 3071 | . . . 4 | |
3 | 2 | abbidv 2288 | . . 3 |
4 | 1, 3 | eqtrd 2203 | . 2 |
5 | df-sn 3589 | . . 3 | |
6 | 5 | csbeq2i 3076 | . 2 |
7 | df-sn 3589 | . 2 | |
8 | 4, 6, 7 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1348 wcel 2141 cab 2156 wsbc 2955 csb 3049 csn 3583 |
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 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-v 2732 df-sbc 2956 df-csb 3050 df-sn 3589 |
This theorem is referenced by: (None) |
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