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Mirrors > Home > ILE Home > Th. List > csbiedf | Unicode version |
Description: Conversion of implicit substitution to explicit substitution into a class. (Contributed by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
csbiedf.1 | |
csbiedf.2 | |
csbiedf.3 | |
csbiedf.4 |
Ref | Expression |
---|---|
csbiedf |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csbiedf.1 | . . 3 | |
2 | csbiedf.4 | . . . 4 | |
3 | 2 | ex 108 | . . 3 |
4 | 1, 3 | alrimi 1415 | . 2 |
5 | csbiedf.3 | . . 3 | |
6 | csbiedf.2 | . . 3 | |
7 | csbiebt 2886 | . . 3 | |
8 | 5, 6, 7 | syl2anc 391 | . 2 |
9 | 4, 8 | mpbid 135 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wnf 1349 wcel 1393 wnfc 2165 csb 2852 |
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-v 2559 df-sbc 2765 df-csb 2853 |
This theorem is referenced by: csbied 2892 csbie2t 2894 |
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