Theorem reurmo 2728

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 2726	. 2 |- ( E! x e. A ph <-> ( E. x e. A ph /\ E* x e. A ph ) )
2	1	simprbi 275	1 |- ( E! x e. A ph -> E* x e. A ph )

Syntax hints:   -> wi 4   E.wrex 2487   E!wreu 2488   E*wrmo 2489

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-eu 2058  df-mo 2059  df-rex 2492  df-reu 2493  df-rmo 2494

This theorem is referenced by: (None)