Theorem nrexrmo 3163

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		pm2.21 120	. 2 |- ( -. E. x e. A ph -> ( E. x e. A ph -> E! x e. A ph ) )
2		rmo5 3162	. 2 |- ( E* x e. A ph <-> ( E. x e. A ph -> E! x e. A ph ) )
3	1, 2	sylibr 224	1 |- ( -. E. x e. A ph -> E* x e. A ph )

Syntax hints:   -. wn 3   -> wi 4   E.wrex 2913   E!wreu 2914   E*wrmo 2915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197  df-mo 2475  df-rex 2918  df-reu 2919  df-rmo 2920

This theorem is referenced by: (None)