Theorem mormo 2640

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 2066	. 2 |- ( E* x ph -> E* x ( x e. A /\ ph ) )
2		df-rmo 2422	. 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. wcel 1480   E*wmo 1998   E*wrmo 2417

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 2000  df-mo 2001  df-rmo 2422

This theorem is referenced by:  reueq  2878  reusv1  4374