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

Theorem ralrimivva 2401
 Description: Inference from Theorem 19.21 of [Margaris] p. 90. (Restricted quantifier version with double quantification.) (Contributed by Jeff Madsen, 19-Jun-2011.)
Hypothesis
Ref Expression
ralrimivva.1 ((𝜑 ∧ (𝑥𝐴𝑦𝐵)) → 𝜓)
Assertion
Ref Expression
ralrimivva (𝜑 → ∀𝑥𝐴𝑦𝐵 𝜓)
Distinct variable groups:   𝜑,𝑥,𝑦   𝑦,𝐴
Allowed substitution hints:   𝜓(𝑥,𝑦)   𝐴(𝑥)   𝐵(𝑥,𝑦)

Proof of Theorem ralrimivva
StepHypRef Expression
1 ralrimivva.1 . . 3 ((𝜑 ∧ (𝑥𝐴𝑦𝐵)) → 𝜓)
21ex 108 . 2 (𝜑 → ((𝑥𝐴𝑦𝐵) → 𝜓))
32ralrimivv 2400 1 (𝜑 → ∀𝑥𝐴𝑦𝐵 𝜓)
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   ∈ 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:  swopo  4043  sosng  4413  fcof1  5423  fliftfund  5437  isoresbr  5449  isocnv  5451  f1oiso  5465  caovclg  5653  caovcomg  5656  off  5724  caofrss  5735  fmpt2co  5837  poxp  5853  eroprf  6199  dom2lem  6252  nnwetri  6354  addlocpr  6634  mullocpr  6669  cauappcvgprlemloc  6750  cauappcvgprlemlim  6759  caucvgprlemloc  6773  caucvgprprlemloc  6801  rereceu  6963  cju  7913  qbtwnz  9106  frec2uzf1od  9192  frec2uzisod  9193  frecuzrdgrrn  9194  iseqcaopr3  9240  iseqcaopr2  9241  iseqhomo  9248  iseqdistr  9249  rsqrmo  9625  climcn2  9830  addcn2  9831  mulcn2  9833
 Copyright terms: Public domain W3C validator