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Mirrors > Home > ILE Home > Th. List > sbciegft | Unicode version |
Description: Conversion of implicit substitution to explicit class substitution, using a bound-variable hypothesis instead of distinct variables. (Closed theorem version of sbciegf 2845.) (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
sbciegft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc5 2838 | . . 3 | |
2 | bi1 116 | . . . . . . . 8 | |
3 | 2 | imim2i 12 | . . . . . . 7 |
4 | 3 | impd 251 | . . . . . 6 |
5 | 4 | alimi 1384 | . . . . 5 |
6 | 19.23t 1607 | . . . . . 6 | |
7 | 6 | biimpa 290 | . . . . 5 |
8 | 5, 7 | sylan2 280 | . . . 4 |
9 | 8 | 3adant1 956 | . . 3 |
10 | 1, 9 | syl5bi 150 | . 2 |
11 | bi2 128 | . . . . . . . 8 | |
12 | 11 | imim2i 12 | . . . . . . 7 |
13 | 12 | com23 77 | . . . . . 6 |
14 | 13 | alimi 1384 | . . . . 5 |
15 | 19.21t 1514 | . . . . . 6 | |
16 | 15 | biimpa 290 | . . . . 5 |
17 | 14, 16 | sylan2 280 | . . . 4 |
18 | 17 | 3adant1 956 | . . 3 |
19 | sbc6g 2839 | . . . 4 | |
20 | 19 | 3ad2ant1 959 | . . 3 |
21 | 18, 20 | sylibrd 167 | . 2 |
22 | 10, 21 | impbid 127 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 w3a 919 wal 1282 wceq 1284 wnf 1389 wex 1421 wcel 1433 wsbc 2815 |
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-3an 921 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 |
This theorem is referenced by: sbciegf 2845 sbciedf 2849 |
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