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Theorem bnj1415 29308
 Description: Technical lemma for bnj60 29332. 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
bnj1415.1
bnj1415.2
bnj1415.3
bnj1415.4
bnj1415.5
bnj1415.6
bnj1415.7
bnj1415.8
bnj1415.9
bnj1415.10
Assertion
Ref Expression
bnj1415
Distinct variable groups:   ,,,   ,   ,   ,   ,,,   ,,   ,   ,
Allowed substitution hints:   (,,)   (,,,)   (,,)   ()   (,,)   (,,)   (,,)   (,,,)   ()   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1415
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1415.7 . . . 4
2 bnj1415.6 . . . . 5
32simplbi 447 . . . 4
41, 3bnj835 29029 . . 3
5 bnj1415.5 . . . 4
65, 1bnj1212 29072 . . 3
7 eqid 2435 . . . 4
87bnj1414 29307 . . 3
94, 6, 8syl2anc 643 . 2
10 iunun 4163 . . . 4
11 iunid 4138 . . . . 5
1211uneq1i 3489 . . . 4
1310, 12eqtri 2455 . . 3
14 bnj1415.1 . . . 4
15 bnj1415.2 . . . 4
16 bnj1415.3 . . . 4
17 bnj1415.4 . . . 4
18 bnj1415.8 . . . 4
19 bnj1415.9 . . . 4
20 bnj1415.10 . . . 4
21 biid 228 . . . 4
22 biid 228 . . . 4
2314, 15, 16, 17, 5, 2, 1, 18, 19, 20, 21, 22bnj1398 29304 . . 3
2413, 23syl5eqr 2481 . 2
259, 24eqtr2d 2468 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 2421   wne 2598  wral 2697  wrex 2698  crab 2701  wsbc 3153   cun 3310   wss 3312  c0 3620  csn 3806  cop 3809  cuni 4007  ciun 4085   class class class wbr 4204   cdm 4870   cres 4872   wfn 5441  cfv 5446   c-bnj14 28953   w-bnj15 28957   c-bnj18 28959 This theorem is referenced by:  bnj1312  29328 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 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693  ax-reg 7550  ax-inf2 7586 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-tr 4295  df-eprel 4486  df-id 4490  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-suc 4579  df-om 4838  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-1o 6716  df-bnj17 28952  df-bnj14 28954  df-bnj13 28956  df-bnj15 28958  df-bnj18 28960  df-bnj19 28962
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