ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2alimi GIF version

Theorem 2alimi 1467
Description: Inference doubly quantifying both antecedent and consequent. (Contributed by NM, 3-Feb-2005.)
Hypothesis
Ref Expression
alimi.1 (𝜑𝜓)
Assertion
Ref Expression
2alimi (∀𝑥𝑦𝜑 → ∀𝑥𝑦𝜓)

Proof of Theorem 2alimi
StepHypRef Expression
1 alimi.1 . . 3 (𝜑𝜓)
21alimi 1466 . 2 (∀𝑦𝜑 → ∀𝑦𝜓)
32alimi 1466 1 (∀𝑥𝑦𝜑 → ∀𝑥𝑦𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wal 1362
This theorem was proved from axioms:  ax-mp 5  ax-5 1458  ax-gen 1460
This theorem is referenced by:  mo23  2083  mo3h  2095  spc2gv  2851  spc3gv  2853  euind  2947  reuind  2965  sbnfc2  3141  opelopabt  4291  ssrel  4743  ssrelrel  4755  fnoprabg  6011
  Copyright terms: Public domain W3C validator