Theorem 2eumo 2085

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 2064	. 2 |- ( A. x ( E! y ph -> E* y ph ) -> ( E! x E* y ph -> E* x E! y ph ) )
2		eumo 2029	. 2 |- ( E! y ph -> E* y ph )
3	1, 2	mpg 1427	1 |- ( E! x E* y ph -> E* x E! y ph )

Syntax hints:   -> wi 4   E!weu 1997   E*wmo 1998

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2000  df-mo 2001

This theorem is referenced by: (None)