Theorem a9e 1632

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 1382 through ax-14 1451 and ax-17 1465, all axioms other than ax-9 1470 are believed to be theorems of free logic, although the system without ax-9 1470 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 1469	1 ⊢ ∃𝑥 𝑥 = 𝑦

Syntax hints:  ∃wex 1427

This theorem was proved from axioms:  ax-i9 1469

This theorem is referenced by:  ax9o  1634  equid  1635  equs4  1661  equsal  1663  equsex  1664  equsexd  1665  spimt  1672  spimeh  1675  spimed  1676  equvini  1689  ax11v2  1749  ax11v  1756  ax11ev  1757  equs5or  1759  euequ1  2044