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

Theorem reubii 2495
Description: Formula-building rule for restricted existential quantifier (inference rule). (Contributed by NM, 22-Oct-1999.)
Hypothesis
Ref Expression
reubii.1 (𝜑𝜓)
Assertion
Ref Expression
reubii (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥𝐴 𝜓)

Proof of Theorem reubii
StepHypRef Expression
1 reubii.1 . . 3 (𝜑𝜓)
21a1i 9 . 2 (𝑥𝐴 → (𝜑𝜓))
32reubiia 2494 1 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 98  wcel 1393  ∃!wreu 2308
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-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-eu 1903  df-reu 2313
This theorem is referenced by:  caucvgsrlemcl  6873  axcaucvglemcl  6969  axcaucvglemval  6971
  Copyright terms: Public domain W3C validator