MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  axie1 Structured version   Visualization version   GIF version

Theorem axie1 2782
Description: The setvar 𝑥 is not free in 𝑥𝜑 (intuitionistic logic axiom ax-ie1). (Contributed by Jim Kingdon, 31-Dec-2017.) (New usage is discouraged.)
Assertion
Ref Expression
axie1 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)

Proof of Theorem axie1
StepHypRef Expression
1 hbe1 2138 1 (∃𝑥𝜑 → ∀𝑥𝑥𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wal 1526  wex 1771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-10 2136
This theorem depends on definitions:  df-bi 208  df-ex 1772
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator