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

Theorem 2ralimi 2471
Description: Inference quantifying both antecedent and consequent two times, with strong hypothesis. (Contributed by AV, 3-Dec-2021.)
Hypothesis
Ref Expression
ralimi.1 (𝜑𝜓)
Assertion
Ref Expression
2ralimi (∀𝑥𝐴𝑦𝐵 𝜑 → ∀𝑥𝐴𝑦𝐵 𝜓)

Proof of Theorem 2ralimi
StepHypRef Expression
1 ralimi.1 . . 3 (𝜑𝜓)
21ralimi 2470 . 2 (∀𝑦𝐵 𝜑 → ∀𝑦𝐵 𝜓)
32ralimi 2470 1 (∀𝑥𝐴𝑦𝐵 𝜑 → ∀𝑥𝐴𝑦𝐵 𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wral 2391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408
This theorem depends on definitions:  df-bi 116  df-ral 2396
This theorem is referenced by:  xmeteq0  12423  xmettri2  12425
  Copyright terms: Public domain W3C validator