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Mirrors > Home > ILE Home > Th. List > hbae | Unicode version |
Description: All variables are effectively bound in an identical variable specifier. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
hbae |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax12or 1490 | . . . 4 | |
2 | ax10o 1693 | . . . . . 6 | |
3 | 2 | alequcoms 1496 | . . . . 5 |
4 | ax10o 1693 | . . . . . . . . 9 | |
5 | 4 | pm2.43i 49 | . . . . . . . 8 |
6 | ax10o 1693 | . . . . . . . 8 | |
7 | 5, 6 | syl5 32 | . . . . . . 7 |
8 | 7 | alequcoms 1496 | . . . . . 6 |
9 | ax-4 1487 | . . . . . . . 8 | |
10 | 9 | imim1i 60 | . . . . . . 7 |
11 | 10 | sps 1517 | . . . . . 6 |
12 | 8, 11 | jaoi 705 | . . . . 5 |
13 | 3, 12 | jaoi 705 | . . . 4 |
14 | 1, 13 | ax-mp 5 | . . 3 |
15 | 14 | a5i 1522 | . 2 |
16 | ax-7 1424 | . 2 | |
17 | 15, 16 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 697 wal 1329 wceq 1331 |
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-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: nfae 1697 hbaes 1698 hbnae 1699 dral1 1708 dral2 1709 drex2 1710 drex1 1770 aev 1784 sbcomxyyz 1943 exists1 2093 |
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