Theorem a9e 1675

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 1424 through ax-14 1493 and ax-17 1507, all axioms other than ax-9 1512 are believed to be theorems of free logic, although the system without ax-9 1512 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 1511	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1469

This theorem was proved from axioms:  ax-i9 1511

This theorem is referenced by:  ax9o  1677  equid  1678  equs4  1704  equsal  1706  equsex  1707  equsexd  1708  spimt  1715  spimeh  1718  spimed  1719  equvini  1732  ax11v2  1793  ax11v  1800  ax11ev  1801  equs5or  1803  euequ1  2095