ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mo23 Structured version   Unicode version

Theorem mo23 1938
Description: An implication between two definitions of "there exists at most one." (Contributed by Jim Kingdon, 25-Jun-2018.)
Hypothesis
Ref Expression
mo23.1  F/
Assertion
Ref Expression
mo23
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem mo23
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 mo23.1 . . . . 5  F/
2 nfv 1418 . . . . 5  F/
31, 2nfim 1461 . . . 4  F/
43nfal 1465 . . 3  F/
5 nfv 1418 . . 3  F/
6 equequ2 1596 . . . . 5
76imbi2d 219 . . . 4
87albidv 1702 . . 3
94, 5, 8cbvex 1636 . 2
10 nfs1v 1812 . . . . . . . 8  F/
11 nfv 1418 . . . . . . . 8  F/
1210, 11nfim 1461 . . . . . . 7  F/
13 sbequ2 1649 . . . . . . . 8
14 ax-8 1392 . . . . . . . 8
1513, 14imim12d 68 . . . . . . 7
163, 12, 15cbv3 1627 . . . . . 6
1716ancli 306 . . . . 5
183nfri 1409 . . . . . 6
1912nfri 1409 . . . . . 6
2018, 19aaanh 1475 . . . . 5
2117, 20sylibr 137 . . . 4
22 prth 326 . . . . . 6
23 equtr2 1594 . . . . . 6
2422, 23syl6 29 . . . . 5
25242alimi 1342 . . . 4
2621, 25syl 14 . . 3
2726exlimiv 1486 . 2
289, 27sylbir 125 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wal 1240   F/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-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-nf 1347  df-sb 1643
This theorem is referenced by:  modc  1940  eu2  1941  eu3h  1942
  Copyright terms: Public domain W3C validator