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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 2935.) (Contributed by NM, 10-Nov-2005.) (Revised by Mario Carneiro, 13-Oct-2016.) |
Ref | Expression |
---|---|
sbciegft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbc5 2927 | . . 3 | |
2 | bi1 117 | . . . . . . . 8 | |
3 | 2 | imim2i 12 | . . . . . . 7 |
4 | 3 | impd 252 | . . . . . 6 |
5 | 4 | alimi 1431 | . . . . 5 |
6 | 19.23t 1655 | . . . . . 6 | |
7 | 6 | biimpa 294 | . . . . 5 |
8 | 5, 7 | sylan2 284 | . . . 4 |
9 | 8 | 3adant1 999 | . . 3 |
10 | 1, 9 | syl5bi 151 | . 2 |
11 | bi2 129 | . . . . . . . 8 | |
12 | 11 | imim2i 12 | . . . . . . 7 |
13 | 12 | com23 78 | . . . . . 6 |
14 | 13 | alimi 1431 | . . . . 5 |
15 | 19.21t 1561 | . . . . . 6 | |
16 | 15 | biimpa 294 | . . . . 5 |
17 | 14, 16 | sylan2 284 | . . . 4 |
18 | 17 | 3adant1 999 | . . 3 |
19 | sbc6g 2928 | . . . 4 | |
20 | 19 | 3ad2ant1 1002 | . . 3 |
21 | 18, 20 | sylibrd 168 | . 2 |
22 | 10, 21 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 962 wal 1329 wceq 1331 wnf 1436 wex 1468 wcel 1480 wsbc 2904 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-sbc 2905 |
This theorem is referenced by: sbciegf 2935 sbciedf 2939 |
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