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Theorem reubii 2675
Description: Formula-building rule for restricted existential quantifier (inference form). (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 2674 1 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 105  wcel 2159  ∃!wreu 2469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-eu 2040  df-reu 2474
This theorem is referenced by:  caucvgsrlemcl  7805  axcaucvglemcl  7911  axcaucvglemval  7913
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