Theorem a9e 1710

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 1461 through ax-14 2170 and ax-17 1540, all axioms other than ax-9 1545 are believed to be theorems of free logic, although the system without ax-9 1545 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 1544	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1506

This theorem was proved from axioms:  ax-i9 1544

This theorem is referenced by:  ax9o  1712  equid  1715  equs4  1739  equsal  1741  equsex  1742  equsexd  1743  spimt  1750  spimeh  1753  spimed  1754  equvini  1772  ax11v2  1834  ax11v  1841  ax11ev  1842  equs5or  1844  euequ1  2140