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Theorem reubii 2797
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 (∃!x A φ∃!x A ψ)

Proof of Theorem reubii
StepHypRef Expression
1 reubii.1 . . 3 (φψ)
21a1i 10 . 2 (x A → (φψ))
32reubiia 2796 1 (∃!x A φ∃!x A ψ)
Colors of variables: wff setvar class
Syntax hints:  wb 176   wcel 1710  ∃!wreu 2616
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208  df-reu 2621
This theorem is referenced by:  2reu5lem1  3041
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