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Mirrors > Home > ILE Home > Th. List > ax11v2 | Unicode version |
Description: Recovery of ax11o 1703 from ax11v 1708 without using ax-11 1397. The hypothesis is even weaker than ax11v 1708, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1703. (Contributed by NM, 2-Feb-2007.) |
Ref | Expression |
---|---|
ax11v2.1 |
Ref | Expression |
---|---|
ax11v2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1586 | . 2 | |
2 | ax11v2.1 | . . . . 5 | |
3 | equequ2 1599 | . . . . . . 7 | |
4 | 3 | adantl 262 | . . . . . 6 |
5 | dveeq2 1696 | . . . . . . . . 9 | |
6 | 5 | imp 115 | . . . . . . . 8 |
7 | hba1 1433 | . . . . . . . . 9 | |
8 | 3 | imbi1d 220 | . . . . . . . . . 10 |
9 | 8 | sps 1430 | . . . . . . . . 9 |
10 | 7, 9 | albidh 1369 | . . . . . . . 8 |
11 | 6, 10 | syl 14 | . . . . . . 7 |
12 | 11 | imbi2d 219 | . . . . . 6 |
13 | 4, 12 | imbi12d 223 | . . . . 5 |
14 | 2, 13 | mpbii 136 | . . . 4 |
15 | 14 | ex 108 | . . 3 |
16 | 15 | exlimdv 1700 | . 2 |
17 | 1, 16 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 97 wb 98 wal 1241 wex 1381 |
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-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 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 df-nf 1350 df-sb 1646 |
This theorem is referenced by: ax11a2 1702 |
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