Theorem a9e 1720

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 1471 through ax-14 2180 and ax-17 1550, all axioms other than ax-9 1555 are believed to be theorems of free logic, although the system without ax-9 1555 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 1554	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1516

This theorem was proved from axioms:  ax-i9 1554

This theorem is referenced by:  ax9o  1722  equid  1725  equs4  1749  equsal  1751  equsex  1752  equsexd  1753  spimt  1760  spimeh  1763  spimed  1764  equvini  1782  ax11v2  1844  ax11v  1851  ax11ev  1852  equs5or  1854  euequ1  2150