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

Theorem ralrimdv 2398
 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 1421 . 2 𝑥𝜑
2 nfv 1421 . 2 𝑥𝜓
3 ralrimdv.1 . 2 (𝜑 → (𝜓 → (𝑥𝐴𝜒)))
41, 2, 3ralrimd 2397 1 (𝜑 → (𝜓 → ∀𝑥𝐴 𝜒))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∈ wcel 1393  ∀wral 2306 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-17 1419 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-ral 2311 This theorem is referenced by:  ralrimdva  2399  ralrimivv  2400  nneneq  6320  fzrevral  8967
 Copyright terms: Public domain W3C validator