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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 2794.) (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
sbciegft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc5 2787 | . . 3 | |
2 | bi1 111 | . . . . . . . 8 | |
3 | 2 | imim2i 12 | . . . . . . 7 |
4 | 3 | impd 242 | . . . . . 6 |
5 | 4 | alimi 1344 | . . . . 5 |
6 | 19.23t 1567 | . . . . . 6 | |
7 | 6 | biimpa 280 | . . . . 5 |
8 | 5, 7 | sylan2 270 | . . . 4 |
9 | 8 | 3adant1 922 | . . 3 |
10 | 1, 9 | syl5bi 141 | . 2 |
11 | bi2 121 | . . . . . . . 8 | |
12 | 11 | imim2i 12 | . . . . . . 7 |
13 | 12 | com23 72 | . . . . . 6 |
14 | 13 | alimi 1344 | . . . . 5 |
15 | 19.21t 1474 | . . . . . 6 | |
16 | 15 | biimpa 280 | . . . . 5 |
17 | 14, 16 | sylan2 270 | . . . 4 |
18 | 17 | 3adant1 922 | . . 3 |
19 | sbc6g 2788 | . . . 4 | |
20 | 19 | 3ad2ant1 925 | . . 3 |
21 | 18, 20 | sylibrd 158 | . 2 |
22 | 10, 21 | impbid 120 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 w3a 885 wal 1241 wceq 1243 wnf 1349 wex 1381 wcel 1393 wsbc 2764 |
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 |
This theorem is referenced by: sbciegf 2794 sbciedf 2798 |
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