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Theorem euorv 1972
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 1462 . 2 (𝜑 → ∀𝑥𝜑)
21euor 1971 1 ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 102  wo 662  ∃!weu 1945
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-eu 1948
This theorem is referenced by:  eueq2dc  2779
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