Theorem euimmo 2066

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 2031	. 2 |- ( E! x ps -> E* x ps )
2		moim 2063	. 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 1329   E!weu 1999   E*wmo 2000

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515

This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2002  df-mo 2003

This theorem is referenced by:  euim  2067  2eumo  2087  reuss2  3356