Theorem nrexrmo 2682

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		pm2.21 607	. 2 |- ( -. E. x e. A ph -> ( E. x e. A ph -> E! x e. A ph ) )
2		rmo5 2681	. 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 2445   E!wreu 2446   E*wrmo 2447

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 605

This theorem depends on definitions:  df-bi 116  df-mo 2018  df-rex 2450  df-reu 2451  df-rmo 2452

This theorem is referenced by: (None)