Theorem reurmo 2645

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 2643	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simprbi 273	1 |- ( E! x e. A ph -> E* x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2417   E!wreu 2418   E*wrmo 2419

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  df-rex 2422  df-reu 2423  df-rmo 2424

This theorem is referenced by: (None)