Theorem 2eumo 2141

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 2120	. 2 |- ( A. x ( E! y ph -> E* y ph ) -> ( E! x E* y ph -> E* x E! y ph ) )
2		eumo 2085	. 2 |- ( E! y ph -> E* y ph )
3	1, 2	mpg 1473	1 |- ( E! x E* y ph -> E* x E! y ph )

Syntax hints:   -> wi 4   E!weu 2053   E*wmo 2054

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-eu 2056  df-mo 2057

This theorem is referenced by: (None)