Theorem 2eumo 2114

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 2093	. 2 |- ( A. x ( E! y ph -> E* y ph ) -> ( E! x E* y ph -> E* x E! y ph ) )
2		eumo 2058	. 2 |- ( E! y ph -> E* y ph )
3	1, 2	mpg 1451	1 |- ( E! x E* y ph -> E* x E! y ph )

Syntax hints:   -> wi 4   E!weu 2026   E*wmo 2027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-eu 2029  df-mo 2030

This theorem is referenced by: (None)