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Theorem a9e 1631
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 1381 through ax-14 1450 and ax-17 1464, all axioms other than ax-9 1469 are believed to be theorems of free logic, although the system without ax-9 1469 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

Proof of Theorem a9e
StepHypRef Expression
1 ax-i9 1468 1 𝑥 𝑥 = 𝑦
Colors of variables: wff set class
Syntax hints:  wex 1426
This theorem was proved from axioms:  ax-i9 1468
This theorem is referenced by:  ax9o  1633  equid  1634  equs4  1660  equsal  1662  equsex  1663  equsexd  1664  spimt  1671  spimeh  1674  spimed  1675  equvini  1688  ax11v2  1748  ax11v  1755  ax11ev  1756  equs5or  1758  euequ1  2043
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