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

Theorem dvelimor 1969
 Description: Disjunctive distinct variable constraint elimination. A user of this theorem starts with a formula (containing ) and a distinct variable constraint between and . The theorem makes it possible to replace the distinct variable constraint with the disjunct ( is just a version of with substituted for ). (Contributed by Jim Kingdon, 11-May-2018.)
Hypotheses
Ref Expression
dvelimor.1
dvelimor.2
Assertion
Ref Expression
dvelimor
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,)   (,)

Proof of Theorem dvelimor
StepHypRef Expression
1 ax-bndl 1469 . . . . . 6
2 orcom 700 . . . . . . 7
32orbi2i 734 . . . . . 6
41, 3mpbi 144 . . . . 5
5 orass 739 . . . . 5
64, 5mpbir 145 . . . 4
7 nfae 1680 . . . . . . 7
8 a16nf 1820 . . . . . . 7
97, 8alrimi 1485 . . . . . 6
10 df-nf 1420 . . . . . . . 8
11 id 19 . . . . . . . . 9
12 dvelimor.1 . . . . . . . . . 10
1312a1i 9 . . . . . . . . 9
1411, 13nfimd 1547 . . . . . . . 8
1510, 14sylbir 134 . . . . . . 7
1615alimi 1414 . . . . . 6
179, 16jaoi 688 . . . . 5
1817orim1i 732 . . . 4
196, 18ax-mp 7 . . 3
20 orcom 700 . . 3
2119, 20mpbi 144 . 2
22 nfalt 1540 . . . 4
23 ax-17 1489 . . . . . 6
24 dvelimor.2 . . . . . 6
2523, 24equsalh 1687 . . . . 5
2625nfbii 1432 . . . 4
2722, 26sylib 121 . . 3
2827orim2i 733 . 2
2921, 28ax-mp 7 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wo 680  wal 1312  wnf 1419 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498 This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719 This theorem is referenced by:  nfsb4or  1974  rgen2a  2460
 Copyright terms: Public domain W3C validator