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Mirrors > Home > ILE Home > Th. List > a9e | Unicode version |
Description: At least one individual exists. This is not a theorem of free logic, which is sound in empty domains. For such a logic, we would add this theorem as an axiom of set theory (Axiom 0 of [Kunen] p. 10). In the system consisting of ax-5 1377 through ax-14 1446 and ax-17 1460, all axioms other than ax-9 1465 are believed to be theorems of free logic, although the system without ax-9 1465 is probably not complete in free logic. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
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a9e |
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Step | Hyp | Ref | Expression |
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1 | ax-i9 1464 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() |
This theorem was proved from axioms: ax-i9 1464 |
This theorem is referenced by: ax9o 1629 equid 1630 equs4 1654 equsal 1656 equsex 1657 equsexd 1658 spimt 1665 spimeh 1668 spimed 1669 equvini 1682 ax11v2 1742 ax11v 1749 ax11ev 1750 equs5or 1752 euequ1 2037 |
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