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

Theorem rspec 2428
Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)
Hypothesis
Ref Expression
rspec.1 𝑥𝐴 𝜑
Assertion
Ref Expression
rspec (𝑥𝐴𝜑)

Proof of Theorem rspec
StepHypRef Expression
1 rspec.1 . 2 𝑥𝐴 𝜑
2 rsp 2424 . 2 (∀𝑥𝐴 𝜑 → (𝑥𝐴𝜑))
31, 2ax-mp 7 1 (𝑥𝐴𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wcel 1439  wral 2360
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-4 1446
This theorem depends on definitions:  df-bi 116  df-ral 2365
This theorem is referenced by:  rspec2  2463  vtoclri  2695  isarep2  5114  ecopover  6404  ecopoverg  6407  indstr  9142
  Copyright terms: Public domain W3C validator