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Theorem euorv 1924
Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euorv ((¬ φ ∃!xψ) → ∃!x(φ ψ))
Distinct variable group:   φ,x
Allowed substitution hint:   ψ(x)

Proof of Theorem euorv
StepHypRef Expression
1 ax-17 1416 . 2 (φxφ)
21euor 1923 1 ((¬ φ ∃!xψ) → ∃!x(φ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97   wo 628  ∃!weu 1897
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248  df-eu 1900
This theorem is referenced by:  eueq2dc  2708
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