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Theorem 2eumo 2683
Description: Double quantification with existential uniqueness and "at most one." (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eumo (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)

Proof of Theorem 2eumo
StepHypRef Expression
1 euimmo 2660 . 2 (∀𝑥(∃!𝑦𝜑 → ∃*𝑦𝜑) → (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑))
2 eumo 2636 . 2 (∃!𝑦𝜑 → ∃*𝑦𝜑)
31, 2mpg 1873 1 (∃!𝑥∃*𝑦𝜑 → ∃*𝑥∃!𝑦𝜑)
Colors of variables: wff setvar class
Syntax hints:  wi 4  ∃!weu 2607  ∃*wmo 2608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-10 2168  ax-12 2196
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-ex 1854  df-nf 1859  df-eu 2611  df-mo 2612
This theorem is referenced by: (None)
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