Theorem a9e 1586

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 1336 through ax-14 1405 and ax-17 1419, all axioms other than ax-9 1424 are believed to be theorems of free logic, although the system without ax-9 1424 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 1423	1 |- E. x x = y

Syntax hints:   E.wex 1381

This theorem was proved from axioms:  ax-i9 1423

This theorem is referenced by:  ax9o  1588  equid  1589  equs4  1613  equsal  1615  equsex  1616  equsexd  1617  spimt  1624  spimeh  1627  spimed  1628  equvini  1641  ax11v2  1701  ax11v  1708  ax11ev  1709  equs5or  1711  euequ1  1995