Theorem mormo 3158

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 2524	. 2 |- ( E* x ph -> E* x ( x e. A /\ ph ) )
2		df-rmo 2920	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
3	1, 2	sylibr 224	1 |- ( E* x ph -> E* x e. A ph )

Syntax hints:   -> wi 4   /\ wa 384   e. wcel 1990   E*wmo 2471   E*wrmo 2915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-ex 1705  df-nf 1710  df-eu 2474  df-mo 2475  df-rmo 2920

This theorem is referenced by:  reueq  3404  reusv1  4866  reusv1OLD  4867  brdom4  9352  phpreu  33393