Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > a9e | GIF 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 1423 through ax-14 1492 and ax-17 1506, all axioms other than ax-9 1511 are believed to be theorems of free logic, although the system without ax-9 1511 is probably not complete in free logic. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.) |
Ref | Expression |
---|---|
a9e | ⊢ ∃𝑥 𝑥 = 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-i9 1510 | 1 ⊢ ∃𝑥 𝑥 = 𝑦 |
Colors of variables: wff set class |
Syntax hints: ∃wex 1468 |
This theorem was proved from axioms: ax-i9 1510 |
This theorem is referenced by: ax9o 1676 equid 1677 equs4 1703 equsal 1705 equsex 1706 equsexd 1707 spimt 1714 spimeh 1717 spimed 1718 equvini 1731 ax11v2 1792 ax11v 1799 ax11ev 1800 equs5or 1802 euequ1 2092 |
Copyright terms: Public domain | W3C validator |