Theorem a9e 1689

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 1440 through ax-14 2144 and ax-17 1519, all axioms other than ax-9 1524 are believed to be theorems of free logic, although the system without ax-9 1524 is probably not complete in free logic. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.)

Assertion

Ref	Expression
a9e	|- E. x x = y

Proof of Theorem a9e

Step	Hyp	Ref	Expression
1		ax-i9 1523	1 |- E. x x = y

Syntax hints:   E.wex 1485

This theorem was proved from axioms:  ax-i9 1523

This theorem is referenced by:  ax9o  1691  equid  1694  equs4  1718  equsal  1720  equsex  1721  equsexd  1722  spimt  1729  spimeh  1732  spimed  1733  equvini  1751  ax11v2  1813  ax11v  1820  ax11ev  1821  equs5or  1823  euequ1  2114