Users' Mathboxes Mathbox for Alexander van der Vekens < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  reuimrmo Unicode version

Theorem reuimrmo 28059
Description: Restricted uniqueness implies restricted "at most one" through implication, analogous to euimmo 2205. (Contributed by Alexander van der Vekens, 25-Jun-2017.)
Assertion
Ref Expression
reuimrmo  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E! x  e.  A  ps  ->  E* x  e.  A ph ) )

Proof of Theorem reuimrmo
StepHypRef Expression
1 reurmo 2768 . 2  |-  ( E! x  e.  A  ps  ->  E* x  e.  A ps )
2 rmoim 2977 . 2  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E* x  e.  A ps  ->  E* x  e.  A ph ) )
31, 2syl5 28 1  |-  ( A. x  e.  A  ( ph  ->  ps )  -> 
( E! x  e.  A  ps  ->  E* x  e.  A ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wral 2556   E!wreu 2558   E*wrmo 2559
This theorem is referenced by:  2reurmo  28063
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-ral 2561  df-rex 2562  df-reu 2563  df-rmo 2564
  Copyright terms: Public domain W3C validator