ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rmo2i Unicode version

Theorem rmo2i 2929
Description: Condition implying restricted at-most-one quantifier. (Contributed by NM, 17-Jun-2017.)
Hypothesis
Ref Expression
rmo2.1  |-  F/ y
ph
Assertion
Ref Expression
rmo2i  |-  ( E. y  e.  A  A. x  e.  A  ( ph  ->  x  =  y )  ->  E* x  e.  A  ph )
Distinct variable group:    x, y, A
Allowed substitution hints:    ph( x, y)

Proof of Theorem rmo2i
StepHypRef Expression
1 rexex 2422 . 2  |-  ( E. y  e.  A  A. x  e.  A  ( ph  ->  x  =  y )  ->  E. y A. x  e.  A  ( ph  ->  x  =  y ) )
2 rmo2.1 . . 3  |-  F/ y
ph
32rmo2ilem 2928 . 2  |-  ( E. y A. x  e.  A  ( ph  ->  x  =  y )  ->  E* x  e.  A  ph )
41, 3syl 14 1  |-  ( E. y  e.  A  A. x  e.  A  ( ph  ->  x  =  y )  ->  E* x  e.  A  ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289   F/wnf 1394   E.wex 1426   A.wral 2359   E.wrex 2360   E*wrmo 2362
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
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-eu 1951  df-mo 1952  df-ral 2364  df-rex 2365  df-rmo 2367
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator