Theorem a9e 1748

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 1500 through ax-14 2212 and ax-17 1579, all axioms other than ax-9 1584 are believed to be theorems of free logic, although the system without ax-9 1584 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 1583	1 |- E. x x = y

Syntax hints:   E.wex 1545

This theorem was proved from axioms:  ax-i9 1583

This theorem is referenced by:  ax9o  1750  equid  1753  equs4  1777  equsal  1779  equsex  1780  equsexd  1782  spimt  1789  spimeh  1792  spimed  1793  equvini  1811  ax11v2  1873  ax11v  1880  ax11ev  1881  equs5or  1883  euequ1  2182