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Mirrors > Home > ILE Home > Th. List > ax11v2 | Unicode version |
Description: Recovery of ax11o 1743 from ax11v 1748 without using ax-11 1437. The hypothesis is even weaker than ax11v 1748, with both distinct from and not occurring in . Thus the hypothesis provides an alternate axiom that can be used in place of ax11o 1743. (Contributed by NM, 2-Feb-2007.) |
Ref | Expression |
---|---|
ax11v2.1 |
Ref | Expression |
---|---|
ax11v2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | a9e 1626 | . 2 | |
2 | ax11v2.1 | . . . . 5 | |
3 | equequ2 1639 | . . . . . . 7 | |
4 | 3 | adantl 271 | . . . . . 6 |
5 | dveeq2 1736 | . . . . . . . . 9 | |
6 | 5 | imp 122 | . . . . . . . 8 |
7 | hba1 1473 | . . . . . . . . 9 | |
8 | 3 | imbi1d 229 | . . . . . . . . . 10 |
9 | 8 | sps 1470 | . . . . . . . . 9 |
10 | 7, 9 | albidh 1409 | . . . . . . . 8 |
11 | 6, 10 | syl 14 | . . . . . . 7 |
12 | 11 | imbi2d 228 | . . . . . 6 |
13 | 4, 12 | imbi12d 232 | . . . . 5 |
14 | 2, 13 | mpbii 146 | . . . 4 |
15 | 14 | ex 113 | . . 3 |
16 | 15 | exlimdv 1740 | . 2 |
17 | 1, 16 | mpi 15 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wal 1282 wex 1421 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in2 577 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 |
This theorem is referenced by: ax11a2 1742 |
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