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Theorem euorv 2002
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 1489 . 2 (𝜑 → ∀𝑥𝜑)
21euor 2001 1 ((¬ 𝜑 ∧ ∃!𝑥𝜓) → ∃!𝑥(𝜑𝜓))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103  wo 680  ∃!weu 1975
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 586  ax-in2 587  ax-io 681  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-eu 1978
This theorem is referenced by:  eueq2dc  2828
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