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

Theorem modc 1940
 Description: Equivalent definitions of "there exists at most one," given decidable existence. (Contributed by Jim Kingdon, 1-Jul-2018.)
Hypothesis
Ref Expression
modc.1
Assertion
Ref Expression
modc DECID
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem modc
StepHypRef Expression
1 modc.1 . . 3
21mo23 1938 . 2
3 exmiddc 743 . . 3 DECID
41mor 1939 . . . 4
51mo2n 1925 . . . . 5
65a1d 22 . . . 4
74, 6jaoi 635 . . 3
83, 7syl 14 . 2 DECID
92, 8impbid2 131 1 DECID
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 97   wb 98   wo 628  DECID wdc 741  wal 1240  wnf 1346  wex 1378  wsb 1642 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425 This theorem depends on definitions:  df-bi 110  df-dc 742  df-tru 1245  df-fal 1248  df-nf 1347  df-sb 1643 This theorem is referenced by:  mo2dc  1952
 Copyright terms: Public domain W3C validator