Theorem mormo 2710

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 2111	. 2 |- ( E* x ph -> E* x ( x e. A /\ ph ) )
2		df-rmo 2480	. 2 |- ( E* x e. A ph <-> E* x ( x e. A /\ ph ) )
3	1, 2	sylibr 134	1 |- ( E* x ph -> E* x e. A ph )

Syntax hints:   -> wi 4   /\ wa 104   E*wmo 2043   e. wcel 2164   E*wrmo 2475

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-eu 2045  df-mo 2046  df-rmo 2480

This theorem is referenced by:  reueq  2959  reusv1  4489