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Theorem euor 2231
 Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.)
Hypothesis
Ref Expression
euor.1 xφ
Assertion
Ref Expression
euor ((¬ φ ∃!xψ) → ∃!x(φ ψ))

Proof of Theorem euor
StepHypRef Expression
1 euor.1 . . . 4 xφ
21nfn 1793 . . 3 x ¬ φ
3 biorf 394 . . 3 φ → (ψ ↔ (φ ψ)))
42, 3eubid 2211 . 2 φ → (∃!xψ∃!x(φ ψ)))
54biimpa 470 1 ((¬ φ ∃!xψ) → ∃!x(φ ψ))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357   ∧ wa 358  Ⅎwnf 1544  ∃!weu 2204 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-eu 2208 This theorem is referenced by:  euorv  2232
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