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

Theorem ralrimdv 2415
Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version.) (Contributed by NM, 27-May-1998.)
Hypothesis
Ref Expression
ralrimdv.1 (𝜑 → (𝜓 → (𝑥𝐴𝜒)))
Assertion
Ref Expression
ralrimdv (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
Distinct variable groups:   𝜑,𝑥   𝜓,𝑥
Allowed substitution hints:   𝜒(𝑥)   𝐴(𝑥)

Proof of Theorem ralrimdv
StepHypRef Expression
1 nfv 1437 . 2 𝑥𝜑
2 nfv 1437 . 2 𝑥𝜓
3 ralrimdv.1 . 2 (𝜑 → (𝜓 → (𝑥𝐴𝜒)))
41, 2, 3ralrimd 2414 1 (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1409  wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-4 1416  ax-17 1435
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-ral 2328
This theorem is referenced by:  ralrimdva  2416  ralrimivv  2417  nneneq  6351  fzrevral  9069
  Copyright terms: Public domain W3C validator