Theorem nrexrmo 2570

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		pm2.21 579	. 2 |- ( -. E. x e. A ph -> ( E. x e. A ph -> E! x e. A ph ) )
2		rmo5 2569	. 2 |- ( E* x e. A ph <-> ( E. x e. A ph -> E! x e. A ph ) )
3	1, 2	sylibr 132	1 |- ( -. E. x e. A ph -> E* x e. A ph )

Syntax hints:   -. wn 3   -> wi 4   E.wrex 2349   E!wreu 2350   E*wrmo 2351

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in2 577

This theorem depends on definitions:  df-bi 115  df-mo 1945  df-rex 2354  df-reu 2355  df-rmo 2356

This theorem is referenced by: (None)