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Mirrors > Home > ILE Home > Th. List > drex1 | Unicode version |
Description: Formula-building lemma for use with the Distinctor Reduction Theorem. Part of Theorem 9.4 of [Megill] p. 448 (p. 16 of preprint). (Contributed by NM, 27-Feb-2005.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
drex1.1 |
Ref | Expression |
---|---|
drex1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbae 1696 | . . . 4 | |
2 | drex1.1 | . . . . 5 | |
3 | ax-4 1487 | . . . . . 6 | |
4 | 3 | biantrurd 303 | . . . . 5 |
5 | 2, 4 | bitr2d 188 | . . . 4 |
6 | 1, 5 | exbidh 1593 | . . 3 |
7 | ax11e 1768 | . . . 4 | |
8 | 7 | sps 1517 | . . 3 |
9 | 6, 8 | sylbird 169 | . 2 |
10 | hbae 1696 | . . . 4 | |
11 | equcomi 1680 | . . . . . . 7 | |
12 | 11 | sps 1517 | . . . . . 6 |
13 | 12 | biantrurd 303 | . . . . 5 |
14 | 13, 2 | bitr3d 189 | . . . 4 |
15 | 10, 14 | exbidh 1593 | . . 3 |
16 | ax11e 1768 | . . . . 5 | |
17 | 16 | sps 1517 | . . . 4 |
18 | 17 | alequcoms 1496 | . . 3 |
19 | 15, 18 | sylbird 169 | . 2 |
20 | 9, 19 | impbid 128 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wceq 1331 wex 1468 |
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-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: drsb1 1771 exdistrfor 1772 copsexg 4166 |
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