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Theorem bnj98 29336
 Description: Technical lemma for bnj150 29345. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj98

Proof of Theorem bnj98
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2965 . . . . . 6
21sucid 4689 . . . . 5
3 n0i 3618 . . . . 5
42, 3ax-mp 5 . . . 4
5 df-suc 4616 . . . . . 6
6 df-un 3311 . . . . . 6
75, 6eqtri 2462 . . . . 5
8 df1o2 6765 . . . . . . 7
97, 8eleq12i 2507 . . . . . 6
10 elsni 3862 . . . . . 6
119, 10sylbi 189 . . . . 5
127, 11syl5eq 2486 . . . 4
134, 12mto 170 . . 3
1413pm2.21i 126 . 2
1514rgenw 2779 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wo 359   wceq 1653   wcel 1727  cab 2428  wral 2711   cun 3304  c0 3613  csn 3838  ciun 4117   csuc 4612  com 4874  cfv 5483  c1o 6746   c-bnj14 29150 This theorem is referenced by:  bnj150  29345 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-v 2964  df-dif 3309  df-un 3311  df-nul 3614  df-sn 3844  df-suc 4616  df-1o 6753
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