Theorem reurmo 2568

Description: Restricted existential uniqueness implies restricted "at most one." (Contributed by NM, 16-Jun-2017.)

Assertion

Ref	Expression
reurmo	|- ( E! x e. A ph -> E* x e. A ph )

Proof of Theorem reurmo

Step	Hyp	Ref	Expression
1		reu5 2566	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simprbi 269	1 |- ( E! x e. A ph -> E* x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2349   E!wreu 2350   E*wrmo 2351

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468

This theorem depends on definitions:  df-bi 115  df-nf 1390  df-sb 1686  df-eu 1944  df-mo 1945  df-rex 2354  df-reu 2355  df-rmo 2356

This theorem is referenced by: (None)