MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axi9 Structured version   Visualization version   GIF version

Theorem axi9 2586
Description: Axiom of existence (intuitionistic logic axiom ax-i9). In classical logic, this is equivalent to ax-6 1875 but in intuitionistic logic it needs to be stated using the existential quantifier. (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)
Ref Expression
axi9 𝑥 𝑥 = 𝑦

Proof of Theorem axi9
StepHypRef Expression
1 ax6e 2238 1 𝑥 𝑥 = 𝑦
Colors of variables: wff setvar class
Syntax hints:  wex 1695
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-12 2034  ax-13 2234
This theorem depends on definitions:  df-bi 196  df-an 385  df-ex 1696
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator