Theorem a9e 1696

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 1447 through ax-14 2151 and ax-17 1526, all axioms other than ax-9 1531 are believed to be theorems of free logic, although the system without ax-9 1531 is probably not complete in free logic. (Contributed by NM, 5-Aug-1993.) (Revised by NM, 3-Feb-2015.)

Assertion

Ref	Expression
a9e	⊢ ∃𝑥 𝑥 = 𝑦

Proof of Theorem a9e

Step	Hyp	Ref	Expression
1		ax-i9 1530	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1492

This theorem was proved from axioms:  ax-i9 1530

This theorem is referenced by:  ax9o  1698  equid  1701  equs4  1725  equsal  1727  equsex  1728  equsexd  1729  spimt  1736  spimeh  1739  spimed  1740  equvini  1758  ax11v2  1820  ax11v  1827  ax11ev  1828  equs5or  1830  euequ1  2121