Theorem 2eumo 1062

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 1045	. 2 ⊢ (∀x(∃!yφ → ∃*yφ) → (∃!x∃*yφ → ∃*x∃!yφ))
2		eumo 1037	. 2 ⊢ (∃!yφ → ∃*yφ)
3	1, 2	mpg 684	1 ⊢ (∃!x∃*yφ → ∃*x∃!yφ)

Syntax hints:   → wi 2  ∃!weu 1007  ∃*wmo 1008

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-7 676  ax-gen 677  ax-8 798  ax-9 799  ax-10 800  ax-11 801  ax-12 802  ax-16 922  ax-17 925

This theorem depends on definitions:  df-bi 128  df-or 197  df-an 198  df-ex 679  df-sb 853  df-eu 1009  df-mo 1010

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