Theorem 2eumo 2394

Description: Double quantification with existential uniqueness and "at most one." (Contributed by NM, 3-Dec-2001.)

Assertion

Ref	Expression
2eumo	|- ( E! x E* y ph -> E* x E! y ph )

Proof of Theorem 2eumo

Step	Hyp	Ref	Expression
1		euimmo 2371	. 2 |- ( A. x ( E! y ph -> E* y ph ) -> ( E! x E* y ph -> E* x E! y ph ) )
2		eumo 2348	. 2 |- ( E! y ph -> E* y ph )
3	1, 2	mpg 1679	1 |- ( E! x E* y ph -> E* x E! y ph )

Syntax hints:   -> wi 4   E!weu 2319   E*wmo 2320

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950

This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672  df-nf 1676  df-eu 2323  df-mo 2324

This theorem is referenced by: (None)