Theorem axi9 2730

Description: Axiom of existence (intuitionistic logic axiom ax-i9). In classical logic, this is equivalent to ax-6 1996 but in intuitionistic logic it needs to be stated using the existential quantifier. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)

Assertion

Ref	Expression
axi9	⊢ ∃𝑥 𝑥 = 𝑦

Proof of Theorem axi9

Step	Hyp	Ref	Expression
1		ax6e 2414	1 ⊢ ∃𝑥 𝑥 = 𝑦

This proof depends on syntax axioms:  ∃wex 1808

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1824  ax-4 1838  ax-5 1939  ax-6 1996  ax-7 2037  ax-12 2212  ax-13 2403

This proof depends on definitions:  df-bi 210  df-an 401  df-ex 1809

This theorem is used by: (None)