Theorem a9e 1684

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 1435 through ax-14 2139 and ax-17 1514, all axioms other than ax-9 1519 are believed to be theorems of free logic, although the system without ax-9 1519 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 1518	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1480

This theorem was proved from axioms:  ax-i9 1518

This theorem is referenced by:  ax9o  1686  equid  1689  equs4  1713  equsal  1715  equsex  1716  equsexd  1717  spimt  1724  spimeh  1727  spimed  1728  equvini  1746  ax11v2  1808  ax11v  1815  ax11ev  1816  equs5or  1818  euequ1  2109