Theorem euimmo 2125

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 2089	. 2 |- ( E! x ps -> E* x ps )
2		moim 2122	. 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 1373   E!weu 2057   E*wmo 2058

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 713  ax-5 1473  ax-7 1474  ax-gen 1475  ax-ie1 1519  ax-ie2 1520  ax-8 1530  ax-10 1531  ax-11 1532  ax-i12 1533  ax-bndl 1535  ax-4 1536  ax-17 1552  ax-i9 1556  ax-ial 1560  ax-i5r 1561

This theorem depends on definitions:  df-bi 117  df-nf 1487  df-sb 1789  df-eu 2060  df-mo 2061

This theorem is referenced by:  euim  2126  2eumo  2146  reuss2  3464