Theorem nrexrmo 2645

Description: Nonexistence implies restricted "at most one". (Contributed by NM, 17-Jun-2017.)

Assertion

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

Proof of Theorem nrexrmo

Step	Hyp	Ref	Expression
1		pm2.21 606	. 2 |- ( -. E. x e. A ph -> ( E. x e. A ph -> E! x e. A ph ) )
2		rmo5 2644	. 2 |- ( E* x e. A ph <-> ( E. x e. A ph -> E! x e. A ph ) )
3	1, 2	sylibr 133	1 |- ( -. E. x e. A ph -> E* x e. A ph )

Syntax hints:   -. wn 3   -> wi 4   E.wrex 2415   E!wreu 2416   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-in2 604

This theorem depends on definitions:  df-bi 116  df-mo 2001  df-rex 2420  df-reu 2421  df-rmo 2422

This theorem is referenced by: (None)