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Theorem bj-inf2vnlem4 13507
 Description: Lemma for bj-inf2vn2 13509. (Contributed by BJ, 8-Dec-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-inf2vnlem4 Ind
Distinct variable groups:   ,,   ,,

Proof of Theorem bj-inf2vnlem4
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bj-inf2vnlem2 13505 . . 3 Ind
2 nfv 1508 . . . 4
3 nfv 1508 . . . 4
4 nfv 1508 . . . 4
5 nfv 1508 . . . 4
6 eleq1 2220 . . . . . 6
7 eleq1 2220 . . . . . 6
86, 7imbi12d 233 . . . . 5
98biimpd 143 . . . 4
10 eleq1 2220 . . . . . 6
11 eleq1 2220 . . . . . 6
1210, 11imbi12d 233 . . . . 5
1312biimprd 157 . . . 4
142, 3, 4, 5, 9, 13setindis 13501 . . 3
151, 14syl6 33 . 2 Ind
16 dfss2 3117 . 2
1715, 16syl6ibr 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 4324  Ind wind 13460 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-setind 4494 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 4330  df-bj-ind 13461 This theorem is referenced by:  bj-inf2vn2  13509
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