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Theorem reubidv 2795
 Description: Formula-building rule for restricted existential quantifier (deduction rule). (Contributed by NM, 17-Oct-1996.)
Hypothesis
Ref Expression
reubidv.1 (φ → (ψχ))
Assertion
Ref Expression
reubidv (φ → (∃!x A ψ∃!x A χ))
Distinct variable group:   φ,x
Allowed substitution hints:   ψ(x)   χ(x)   A(x)

Proof of Theorem reubidv
StepHypRef Expression
1 reubidv.1 . . 3 (φ → (ψχ))
21adantr 451 . 2 ((φ x A) → (ψχ))
32reubidva 2794 1 (φ → (∃!x A ψ∃!x A χ))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ↔ 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-ex 1542  df-nf 1545  df-eu 2208  df-reu 2621 This theorem is referenced by:  reueqd  2817  sbcreug  3122
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