Theorem a9e 1742

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 1493 through ax-14 2203 and ax-17 1572, all axioms other than ax-9 1577 are believed to be theorems of free logic, although the system without ax-9 1577 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 1576	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1538

This theorem was proved from axioms:  ax-i9 1576

This theorem is referenced by:  ax9o  1744  equid  1747  equs4  1771  equsal  1773  equsex  1774  equsexd  1775  spimt  1782  spimeh  1785  spimed  1786  equvini  1804  ax11v2  1866  ax11v  1873  ax11ev  1874  equs5or  1876  euequ1  2173