ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-ial GIF version

Axiom ax-ial 1527
Description: 𝑥 is not free in 𝑥𝜑. One of the axioms of predicate logic. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-ial (∀𝑥𝜑 → ∀𝑥𝑥𝜑)

Detailed syntax breakdown of Axiom ax-ial
StepHypRef Expression
1 wph . . 3 wff 𝜑
2 vx . . 3 setvar 𝑥
31, 2wal 1346 . 2 wff 𝑥𝜑
43, 2wal 1346 . 2 wff 𝑥𝑥𝜑
53, 4wi 4 1 wff (∀𝑥𝜑 → ∀𝑥𝑥𝜑)
Colors of variables: wff set class
This axiom is referenced by:  hba1  1533  ax6b  1644  exdistrfor  1793  sbcof2  1803  hbs1  1931  sbcomxyyz  1965
  Copyright terms: Public domain W3C validator