ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  ax-i5r GIF version

Axiom ax-i5r 1469
Description: Axiom of quantifier collection. (Contributed by Mario Carneiro, 31-Jan-2015.)
Assertion
Ref Expression
ax-i5r ((∀𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(∀𝑥𝜑𝜓))

Detailed syntax breakdown of Axiom ax-i5r
StepHypRef Expression
1 wph . . . 4 wff 𝜑
2 vx . . . 4 setvar 𝑥
31, 2wal 1283 . . 3 wff 𝑥𝜑
4 wps . . . 4 wff 𝜓
54, 2wal 1283 . . 3 wff 𝑥𝜓
63, 5wi 4 . 2 wff (∀𝑥𝜑 → ∀𝑥𝜓)
73, 4wi 4 . . 3 wff (∀𝑥𝜑𝜓)
87, 2wal 1283 . 2 wff 𝑥(∀𝑥𝜑𝜓)
96, 8wi 4 1 wff ((∀𝑥𝜑 → ∀𝑥𝜓) → ∀𝑥(∀𝑥𝜑𝜓))
Colors of variables: wff set class
This axiom is referenced by:  hbim  1478  hbimd  1506
  Copyright terms: Public domain W3C validator