Theorem euimmo 2112

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 2077	. 2 |- ( E! x ps -> E* x ps )
2		moim 2109	. 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 1362   E!weu 2045   E*wmo 2046

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549

This theorem depends on definitions:  df-bi 117  df-nf 1475  df-sb 1777  df-eu 2048  df-mo 2049

This theorem is referenced by:  euim  2113  2eumo  2133  reuss2  3443