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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 1403 | . . . 4 | |
2 | ax10o 1603 | . . . . . 6 | |
3 | 2 | alequcoms 1409 | . . . . 5 |
4 | ax10o 1603 | . . . . . . . . 9 | |
5 | 4 | pm2.43i 43 | . . . . . . . 8 |
6 | ax10o 1603 | . . . . . . . 8 | |
7 | 5, 6 | syl5 28 | . . . . . . 7 |
8 | 7 | alequcoms 1409 | . . . . . 6 |
9 | ax-4 1400 | . . . . . . . 8 | |
10 | 9 | imim1i 54 | . . . . . . 7 |
11 | 10 | sps 1430 | . . . . . 6 |
12 | 8, 11 | jaoi 636 | . . . . 5 |
13 | 3, 12 | jaoi 636 | . . . 4 |
14 | 1, 13 | ax-mp 7 | . . 3 |
15 | 14 | a5i 1435 | . 2 |
16 | ax-7 1337 | . 2 | |
17 | 15, 16 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wo 629 wal 1241 wceq 1243 |
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-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: nfae 1607 hbaes 1608 hbnae 1609 dral1 1618 dral2 1619 drex2 1620 drex1 1679 aev 1693 sbcomxyyz 1846 exists1 1996 |
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