Theorem 2eumo 2545

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 2522	. 2 |- ( A. x ( E! y ph -> E* y ph ) -> ( E! x E* y ph -> E* x E! y ph ) )
2		eumo 2499	. 2 |- ( E! y ph -> E* y ph )
3	1, 2	mpg 1724	1 |- ( E! x E* y ph -> E* x E! y ph )

Syntax hints:   -> wi 4   E!weu 2470   E*wmo 2471

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475

This theorem is referenced by: (None)