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Mirrors > Home > ILE Home > Th. List > ax10o | Unicode version |
Description: Show that ax-10o 1709 can be derived from ax-10 1498. An open problem is
whether this theorem can be derived from ax-10 1498 and the others when
ax-11 1499 is replaced with ax-11o 1816. See Theorem ax10 1710
for the
rederivation of ax-10 1498 from ax10o 1708.
Normally, ax10o 1708 should be used rather than ax-10o 1709, except by theorems specifically studying the latter's properties. (Contributed by NM, 16-May-2008.) |
Ref | Expression |
---|---|
ax10o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-10 1498 | . 2 | |
2 | ax-11 1499 | . . . 4 | |
3 | 2 | equcoms 1701 | . . 3 |
4 | 3 | sps 1530 | . 2 |
5 | pm2.27 40 | . . 3 | |
6 | 5 | al2imi 1451 | . 2 |
7 | 1, 4, 6 | sylsyld 58 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wal 1346 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-5 1440 ax-gen 1442 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: hbae 1711 dral1 1723 |
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