Theorem 2eumo 1445

Description: Double quantification with existential uniqueness and "at most one."

Assertion

Ref	Expression
2eumo	⊢ (∃!x∃*yφ → ∃*x∃!yφ)

Proof of Theorem 2eumo

Step	Hyp	Ref	Expression
1		euimmo 1422	. 2 ⊢ (∀x(∃!yφ → ∃*yφ) → (∃!x∃*yφ → ∃*x∃!yφ))
2		eumo 1413	. 2 ⊢ (∃!yφ → ∃*yφ)
3	1, 2	mpg 988	1 ⊢ (∃!x∃*yφ → ∃*x∃!yφ)

Syntax hints:   → wi 3  ∃!weu 1382  ∃*wmo 1383

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 964  ax-gen 965  ax-8 966  ax-10 968  ax-11 969  ax-12 970  ax-17 973  ax-4 975  ax-5o 977  ax-6o 980  ax-9o 1125  ax-10o 1142  ax-16 1212  ax-11o 1220

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 983  df-sb 1174  df-eu 1384  df-mo 1385

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