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Theorem 2eumo 2720
Description: Nested unique existential quantifier and at-most-one quantifier. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eumo (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)

Proof of Theorem 2eumo
StepHypRef Expression
1 euimmo 2693 . 2 (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑))
2 eumo 2656 . 2 (∃!𝑦𝜑 → ∃*𝑦𝜑)
31, 2mpg 1789 1 (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2613  ∃!weu 2646
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-mo 2615  df-eu 2647
This theorem is referenced by: (None)
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