Theorem nrexrmo 2526

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		pm2.21 547	. 2 |- ( -. E. x e. A ph -> ( E. x e. A ph -> E! x e. A ph ) )
2		rmo5 2525	. 2 |- ( E* x e. A ph <-> ( E. x e. A ph -> E! x e. A ph ) )
3	1, 2	sylibr 137	1 |- ( -. E. x e. A ph -> E* x e. A ph )

Syntax hints:   -. wn 3   -> wi 4   E.wrex 2307   E!wreu 2308   E*wrmo 2309

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in2 545

This theorem depends on definitions:  df-bi 110  df-mo 1904  df-rex 2312  df-reu 2313  df-rmo 2314

This theorem is referenced by: (None)