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Mirrors > Home > ILE Home > Th. List > csbiebt | Unicode version |
Description: Conversion of implicit substitution to explicit substitution into a class. (Closed theorem version of csbiegf 2890.) (Contributed by NM, 11-Nov-2005.) |
Ref | Expression |
---|---|
csbiebt |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2566 | . 2 | |
2 | spsbc 2775 | . . . . 5 | |
3 | 2 | adantr 261 | . . . 4 |
4 | simpl 102 | . . . . 5 | |
5 | biimt 230 | . . . . . . 7 | |
6 | csbeq1a 2860 | . . . . . . . 8 | |
7 | 6 | eqeq1d 2048 | . . . . . . 7 |
8 | 5, 7 | bitr3d 179 | . . . . . 6 |
9 | 8 | adantl 262 | . . . . 5 |
10 | nfv 1421 | . . . . . 6 | |
11 | nfnfc1 2181 | . . . . . 6 | |
12 | 10, 11 | nfan 1457 | . . . . 5 |
13 | nfcsb1v 2882 | . . . . . . 7 | |
14 | 13 | a1i 9 | . . . . . 6 |
15 | simpr 103 | . . . . . 6 | |
16 | 14, 15 | nfeqd 2192 | . . . . 5 |
17 | 4, 9, 12, 16 | sbciedf 2798 | . . . 4 |
18 | 3, 17 | sylibd 138 | . . 3 |
19 | 13 | a1i 9 | . . . . . . . 8 |
20 | id 19 | . . . . . . . 8 | |
21 | 19, 20 | nfeqd 2192 | . . . . . . 7 |
22 | 11, 21 | nfan1 1456 | . . . . . 6 |
23 | 7 | biimprcd 149 | . . . . . . 7 |
24 | 23 | adantl 262 | . . . . . 6 |
25 | 22, 24 | alrimi 1415 | . . . . 5 |
26 | 25 | ex 108 | . . . 4 |
27 | 26 | adantl 262 | . . 3 |
28 | 18, 27 | impbid 120 | . 2 |
29 | 1, 28 | sylan 267 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wceq 1243 wcel 1393 wnfc 2165 cvv 2557 wsbc 2764 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: csbiedf 2887 csbieb 2888 csbiegf 2890 |
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