Theorem mormo 2677

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

Assertion

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

Proof of Theorem mormo

Step	Hyp	Ref	Expression
1		moan 2083	. 2 |- ( E* x ph -> E* x ( x e. A /\ ph ) )
2		df-rmo 2452	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
3	1, 2	sylibr 133	1 |- ( E* x ph -> E* x e. A ph )

Syntax hints:   -> wi 4   /\ wa 103   E*wmo 2015   e. wcel 2136   E*wrmo 2447

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 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-eu 2017  df-mo 2018  df-rmo 2452

This theorem is referenced by:  reueq  2925  reusv1  4436