Mathbox for BJ < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-inf2vnlem3 Unicode version

Theorem bj-inf2vnlem3 13518
 Description: Lemma for bj-inf2vn 13520. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-inf2vnlem3.bd1 BOUNDED
bj-inf2vnlem3.bd2 BOUNDED
Assertion
Ref Expression
bj-inf2vnlem3 Ind
Distinct variable groups:   ,,   ,,

Proof of Theorem bj-inf2vnlem3
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bj-inf2vnlem2 13517 . . 3 Ind
2 bj-inf2vnlem3.bd1 . . . . . 6 BOUNDED
32bdeli 13392 . . . . 5 BOUNDED
4 bj-inf2vnlem3.bd2 . . . . . 6 BOUNDED
54bdeli 13392 . . . . 5 BOUNDED
63, 5ax-bdim 13360 . . . 4 BOUNDED
7 nfv 1508 . . . 4
8 nfv 1508 . . . 4
9 nfv 1508 . . . 4
10 nfv 1508 . . . 4
11 eleq1 2220 . . . . . 6
12 eleq1 2220 . . . . . 6
1311, 12imbi12d 233 . . . . 5
1413biimpd 143 . . . 4
15 eleq1 2220 . . . . . 6
16 eleq1 2220 . . . . . 6
1715, 16imbi12d 233 . . . . 5
1817biimprd 157 . . . 4
196, 7, 8, 9, 10, 14, 18bdsetindis 13515 . . 3
201, 19syl6 33 . 2 Ind
21 dfss2 3117 . 2
2220, 21syl6ibr 161 1 Ind
 Colors of variables: wff set class Syntax hints:   wi 4   wo 698  wal 1333   wceq 1335   wcel 2128  wral 2435  wrex 2436   wss 3102  c0 3394   csuc 4325  BOUNDED wbdc 13386  Ind wind 13472 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-bdim 13360  ax-bdsetind 13514 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-ral 2440  df-rex 2441  df-v 2714  df-un 3106  df-in 3108  df-ss 3115  df-sn 3566  df-suc 4331  df-bdc 13387  df-bj-ind 13473 This theorem is referenced by:  bj-inf2vn  13520
 Copyright terms: Public domain W3C validator