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Mirrors > Home > ILE Home > Th. List > sbccomlem | Unicode version |
Description: Lemma for sbccom 2979. (Contributed by NM, 14-Nov-2005.) (Revised by Mario Carneiro, 18-Oct-2016.) |
Ref | Expression |
---|---|
sbccomlem |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | excom 1642 | . . . 4 | |
2 | exdistr 1881 | . . . 4 | |
3 | an12 550 | . . . . . . 7 | |
4 | 3 | exbii 1584 | . . . . . 6 |
5 | 19.42v 1878 | . . . . . 6 | |
6 | 4, 5 | bitri 183 | . . . . 5 |
7 | 6 | exbii 1584 | . . . 4 |
8 | 1, 2, 7 | 3bitr3i 209 | . . 3 |
9 | sbc5 2927 | . . 3 | |
10 | sbc5 2927 | . . 3 | |
11 | 8, 9, 10 | 3bitr4i 211 | . 2 |
12 | sbc5 2927 | . . 3 | |
13 | 12 | sbcbii 2963 | . 2 |
14 | sbc5 2927 | . . 3 | |
15 | 14 | sbcbii 2963 | . 2 |
16 | 11, 13, 15 | 3bitr4i 211 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wex 1468 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-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: sbccom 2979 |
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