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Theorem bnj929 29759
 Description: Technical lemma for bnj69 29831. 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.)
Hypotheses
Ref Expression
bnj929.1
bnj929.4
bnj929.7
bnj929.10
bnj929.13
bnj929.50
Assertion
Ref Expression
bnj929
Distinct variable groups:   ,,   ,,   ,,
Allowed substitution hints:   (,,)   ()   (,,)   (,,)   ()   (,,)   ()   (,,)   (,,)

Proof of Theorem bnj929
StepHypRef Expression
1 bnj645 29572 . 2
2 bnj334 29530 . . . . . . 7
3 bnj257 29524 . . . . . . 7
42, 3bitri 253 . . . . . 6
5 bnj345 29531 . . . . . 6
6 bnj253 29521 . . . . . 6
74, 5, 63bitri 275 . . . . 5
87simp1bi 1024 . . . 4
9 bnj929.13 . . . . . 6
10 bnj929.50 . . . . . 6
119, 10bnj927 29592 . . . . 5
1211bnj930 29593 . . . 4
138, 12syl 17 . . 3
149bnj931 29594 . . . 4
1514a1i 11 . . 3
16 bnj268 29526 . . . . . 6
17 bnj253 29521 . . . . . 6
1816, 17bitr3i 255 . . . . 5
1918simp1bi 1024 . . . 4
20 fndm 5680 . . . . 5
21 bnj929.10 . . . . . 6
2221bnj529 29563 . . . . 5
23 eleq2 2520 . . . . . 6
2423biimpar 488 . . . . 5
2520, 22, 24syl2anr 481 . . . 4
2619, 25syl 17 . . 3
2713, 15, 26bnj1502 29671 . 2
28 bnj929.1 . . 3
29 bnj929.4 . . 3
30 bnj929.7 . . 3
319bnj918 29589 . . 3
3228, 29, 30, 31bnj934 29758 . 2
331, 27, 32syl2anc 667 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 188   wa 371   w3a 986   wceq 1446   wcel 1889  cvv 3047  wsbc 3269   cdif 3403   cun 3404   wss 3406  c0 3733  csn 3970  cop 3976   cdm 4837   csuc 5428   wfun 5579   wfn 5580  cfv 5585  com 6697   w-bnj17 29503   c-bnj14 29505 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-8 1891  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642  ax-un 6588  ax-reg 8112 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 987  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-eu 2305  df-mo 2306  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-sbc 3270  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-pss 3422  df-nul 3734  df-if 3884  df-pw 3955  df-sn 3971  df-pr 3973  df-tp 3975  df-op 3977  df-uni 4202  df-br 4406  df-opab 4465  df-tr 4501  df-eprel 4748  df-id 4752  df-po 4758  df-so 4759  df-fr 4796  df-we 4798  df-xp 4843  df-rel 4844  df-cnv 4845  df-co 4846  df-dm 4847  df-res 4849  df-ord 5429  df-on 5430  df-lim 5431  df-suc 5432  df-iota 5549  df-fun 5587  df-fn 5588  df-fv 5593  df-om 6698  df-bnj17 29504 This theorem is referenced by:  bnj944  29761
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