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Mirrors > Home > ILE Home > Th. List > ax10o | Unicode version |
Description: Show that ax-10o 1716 can be derived from ax-10 1505. An open problem is
whether this theorem can be derived from ax-10 1505 and the others when
ax-11 1506 is replaced with ax-11o 1823. See Theorem ax10 1717
for the
rederivation of ax-10 1505 from ax10o 1715.
Normally, ax10o 1715 should be used rather than ax-10o 1716, except by theorems specifically studying the latter's properties. (Contributed by NM, 16-May-2008.) |
Ref | Expression |
---|---|
ax10o |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-10 1505 |
. 2
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2 | ax-11 1506 |
. . . 4
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3 | 2 | equcoms 1708 |
. . 3
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4 | 3 | sps 1537 |
. 2
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5 | pm2.27 40 |
. . 3
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6 | 5 | al2imi 1458 |
. 2
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7 | 1, 4, 6 | sylsyld 58 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-5 1447 ax-gen 1449 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-4 1510 ax-17 1526 ax-i9 1530 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: hbae 1718 dral1 1730 |
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