Theorem a9e 1627

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 1377 through ax-14 1446 and ax-17 1460, all axioms other than ax-9 1465 are believed to be theorems of free logic, although the system without ax-9 1465 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 1464	1 |- E. x x = y

Syntax hints:   E.wex 1422

This theorem was proved from axioms:  ax-i9 1464

This theorem is referenced by:  ax9o  1629  equid  1630  equs4  1654  equsal  1656  equsex  1657  equsexd  1658  spimt  1665  spimeh  1668  spimed  1669  equvini  1682  ax11v2  1742  ax11v  1749  ax11ev  1750  equs5or  1752  euequ1  2037