Theorem a9e 1655

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 1404 through ax-14 1473 and ax-17 1487, all axioms other than ax-9 1492 are believed to be theorems of free logic, although the system without ax-9 1492 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 1491	1 |- E. x x = y

Syntax hints:   E.wex 1449

This theorem was proved from axioms:  ax-i9 1491

This theorem is referenced by:  ax9o  1657  equid  1658  equs4  1684  equsal  1686  equsex  1687  equsexd  1688  spimt  1695  spimeh  1698  spimed  1699  equvini  1712  ax11v2  1772  ax11v  1779  ax11ev  1780  equs5or  1782  euequ1  2068