Theorem euimmo 2145

Description: Uniqueness implies "at most one" through implication. (Contributed by NM, 22-Apr-1995.)

Assertion

Ref	Expression
euimmo	|- ( A. x ( ph -> ps ) -> ( E! x ps -> E* x ph ) )

Proof of Theorem euimmo

Step	Hyp	Ref	Expression
1		eumo 2109	. 2 |- ( E! x ps -> E* x ps )
2		moim 2142	. 2 |- ( A. x ( ph -> ps ) -> ( E* x ps -> E* x ph ) )
3	1, 2	syl5 32	1 |- ( A. x ( ph -> ps ) -> ( E! x ps -> E* x ph ) )

Syntax hints:   -> wi 4   A.wal 1393   E!weu 2077   E*wmo 2078

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-eu 2080  df-mo 2081

This theorem is referenced by:  euim  2146  2eumo  2166  reuss2  3484