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Theorem bdrmo 11747
Description: Boundedness of existential at-most-one. (Contributed by BJ, 16-Oct-2019.)
Hypothesis
Ref Expression
bdrmo.1  |- BOUNDED  ph
Assertion
Ref Expression
bdrmo  |- BOUNDED  E* x  e.  y 
ph
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem bdrmo
StepHypRef Expression
1 bdrmo.1 . . . 4  |- BOUNDED  ph
21ax-bdex 11710 . . 3  |- BOUNDED  E. x  e.  y 
ph
31bdreu 11746 . . 3  |- BOUNDED  E! x  e.  y 
ph
42, 3ax-bdim 11705 . 2  |- BOUNDED  ( E. x  e.  y  ph  ->  E! x  e.  y  ph )
5 rmo5 2582 . 2  |-  ( E* x  e.  y  ph  <->  ( E. x  e.  y 
ph  ->  E! x  e.  y  ph ) )
64, 5bd0r 11716 1  |- BOUNDED  E* x  e.  y 
ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wrex 2360   E!wreu 2361   E*wrmo 2362  BOUNDED wbd 11703
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-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bd0 11704  ax-bdim 11705  ax-bdan 11706  ax-bdal 11709  ax-bdex 11710  ax-bdeq 11711
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-cleq 2081  df-clel 2084  df-ral 2364  df-rex 2365  df-reu 2366  df-rmo 2367
This theorem is referenced by: (None)
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