Theorem mormo 2521

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 1969	. 2 |- ( E* x ph -> E* x ( x e. A /\ ph ) )
2		df-rmo 2314	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
3	1, 2	sylibr 137	1 |- ( E* x ph -> E* x e. A ph )

Syntax hints:   -> wi 4   /\ wa 97   e. wcel 1393   E*wmo 1901   E*wrmo 2309

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428

This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-rmo 2314

This theorem is referenced by:  reueq  2738  reusv1  4190