Theorem reurmo 2725

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 2723	. 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 2485   E!wreu 2486   E*wrmo 2487

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-eu 2057  df-mo 2058  df-rex 2490  df-reu 2491  df-rmo 2492

This theorem is referenced by: (None)