Theorem a9e 1719

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 1470 through ax-14 2179 and ax-17 1549, all axioms other than ax-9 1554 are believed to be theorems of free logic, although the system without ax-9 1554 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 1553	1 |- E. x x = y

Syntax hints:   E.wex 1515

This theorem was proved from axioms:  ax-i9 1553

This theorem is referenced by:  ax9o  1721  equid  1724  equs4  1748  equsal  1750  equsex  1751  equsexd  1752  spimt  1759  spimeh  1762  spimed  1763  equvini  1781  ax11v2  1843  ax11v  1850  ax11ev  1851  equs5or  1853  euequ1  2149