Theorem a9e 1626

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 1376 through ax-14 1445 and ax-17 1459, all axioms other than ax-9 1464 are believed to be theorems of free logic, although the system without ax-9 1464 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 1463	1 |- E. x x = y

Syntax hints:   E.wex 1421

This theorem was proved from axioms:  ax-i9 1463

This theorem is referenced by:  ax9o  1628  equid  1629  equs4  1653  equsal  1655  equsex  1656  equsexd  1657  spimt  1664  spimeh  1667  spimed  1668  equvini  1681  ax11v2  1741  ax11v  1748  ax11ev  1749  equs5or  1751  euequ1  2036