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Theorem 2eumo 2723
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 2696 . 2 (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑))
2 eumo 2659 . 2 (∃!𝑦𝜑 → ∃*𝑦𝜑)
31, 2mpg 1794 1 (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2616  ∃!weu 2649
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1907
This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1777  df-mo 2618  df-eu 2650
This theorem is referenced by: (None)
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