Theorem 2eumo 2277

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

Step	Hyp	Ref	Expression
1		euimmo 2253	. 2 ⊢ (∀x(∃!yφ → ∃*yφ) → (∃!x∃*yφ → ∃*x∃!yφ))
2		eumo 2244	. 2 ⊢ (∃!yφ → ∃*yφ)
3	1, 2	mpg 1548	1 ⊢ (∃!x∃*yφ → ∃*x∃!yφ)

Syntax hints:   → wi 4  ∃!weu 2204  ∃*wmo 2205

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-mo 2209

This theorem is referenced by: (None)