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Theorem euorv 2046
Description: Introduce a disjunct into a unique existential quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euorv ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑𝜓))
Distinct variable group:   𝜑,𝑥
Allowed substitution hint:   𝜓(𝑥)

Proof of Theorem euorv
StepHypRef Expression
1 ax-17 1519 . 2 (𝜑 → ∀𝑥𝜑)
21euor 2045 1 ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103  wo 703  ∃!weu 2019
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-io 704  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354  df-eu 2022
This theorem is referenced by:  eueq2dc  2903
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