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Theorem nrexrmo 2927
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
StepHypRef Expression
1 pm2.21 103 . 2  |-  ( -. 
E. x  e.  A  ph 
->  ( E. x  e.  A  ph  ->  E! x  e.  A  ph )
)
2 rmo5 2926 . 2  |-  ( E* x  e.  A ph  <->  ( E. x  e.  A  ph 
->  E! x  e.  A  ph ) )
31, 2sylibr 205 1  |-  ( -. 
E. x  e.  A  ph 
->  E* x  e.  A ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   E.wrex 2708   E!wreu 2709   E*wrmo 2710
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 179  df-mo 2288  df-rex 2713  df-reu 2714  df-rmo 2715
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