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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
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