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Theorem 2eumo 2643
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 2617 . 2 (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑))
2 eumo 2577 . 2 (∃!𝑦𝜑 → ∃*𝑦𝜑)
31, 2mpg 1805 1 (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃*wmo 2537  ∃!weu 2567
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918
This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1788  df-mo 2539  df-eu 2568
This theorem is referenced by: (None)
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