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Theorem reubii 2552
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 2551 1 (∃!𝑥𝐴 𝜑 ↔ ∃!𝑥𝐴 𝜓)
Colors of variables: wff set class
Syntax hints:  wb 103  wcel 1438  ∃!wreu 2361
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-eu 1951  df-reu 2366
This theorem is referenced by:  caucvgsrlemcl  7332  axcaucvglemcl  7428  axcaucvglemval  7430
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