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Theorem bnj1421 29411
 Description: Technical lemma for bnj60 29431. 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
bnj1421.1
bnj1421.2
bnj1421.3
bnj1421.4
bnj1421.5
bnj1421.6
bnj1421.7
bnj1421.8
bnj1421.9
bnj1421.10
bnj1421.11
bnj1421.12
bnj1421.13
bnj1421.14
bnj1421.15
Assertion
Ref Expression
bnj1421
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1421
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1421.13 . . . 4
2 vex 2959 . . . . 5
3 fvex 5742 . . . . 5
42, 3funsn 5499 . . . 4
51, 4jctir 525 . . 3
6 bnj1421.15 . . . . 5
73dmsnop 5344 . . . . . 6
87a1i 11 . . . . 5
96, 8ineq12d 3543 . . . 4
10 bnj1421.7 . . . . . . 7
11 bnj1421.6 . . . . . . . 8
1211simplbi 447 . . . . . . 7
1310, 12bnj835 29128 . . . . . 6
14 biid 228 . . . . . . . 8
15 biid 228 . . . . . . . 8
16 biid 228 . . . . . . . 8
17 biid 228 . . . . . . . 8
18 eqid 2436 . . . . . . . 8
1914, 15, 16, 17, 18bnj1417 29410 . . . . . . 7
20 disjsn 3868 . . . . . . . 8
2120ralbii 2729 . . . . . . 7
2219, 21sylibr 204 . . . . . 6
2313, 22syl 16 . . . . 5
24 bnj1421.5 . . . . . 6
2524, 10bnj1212 29171 . . . . 5
2623, 25bnj1294 29189 . . . 4
279, 26eqtrd 2468 . . 3
28 funun 5495 . . 3
295, 27, 28syl2anc 643 . 2
30 bnj1421.12 . . 3
3130funeqi 5474 . 2
3229, 31sylibr 204 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422   wne 2599  wral 2705  wrex 2706  crab 2709  wsbc 3161   cun 3318   cin 3319   wss 3320  c0 3628  csn 3814  cop 3817  cuni 4015  ciun 4093   class class class wbr 4212   cdm 4878   cres 4880   wfun 5448   wfn 5449  cfv 5454   c-bnj14 29052   w-bnj15 29056   c-bnj18 29058 This theorem is referenced by:  bnj1312  29427 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-rep 4320  ax-sep 4330  ax-nul 4338  ax-pow 4377  ax-pr 4403  ax-un 4701  ax-reg 7560  ax-inf2 7596 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-reu 2712  df-rab 2714  df-v 2958  df-sbc 3162  df-csb 3252  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-pss 3336  df-nul 3629  df-if 3740  df-pw 3801  df-sn 3820  df-pr 3821  df-tp 3822  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-mpt 4268  df-tr 4303  df-eprel 4494  df-id 4498  df-po 4503  df-so 4504  df-fr 4541  df-we 4543  df-ord 4584  df-on 4585  df-lim 4586  df-suc 4587  df-om 4846  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461  df-fv 5462  df-1o 6724  df-bnj17 29051  df-bnj14 29053  df-bnj13 29055  df-bnj15 29057  df-bnj18 29059  df-bnj19 29061
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