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Theorem bnj518 33240
 Description: Technical lemma for bnj852 33275. 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
bnj518.1
bnj518.2
bnj518.3
Assertion
Ref Expression
bnj518
Distinct variable groups:   ,,,   ,,   ,,,   ,
Allowed substitution hints:   (,,,,,)   (,,,,,)   (,,,,,)   (,,)   (,,,,)

Proof of Theorem bnj518
StepHypRef Expression
1 bnj518.3 . . . 4
2 bnj334 33062 . . . 4
31, 2bitri 249 . . 3
4 df-bnj17 33036 . . . 4
5 bnj518.1 . . . . . 6
6 bnj518.2 . . . . . 6
75, 6bnj517 33239 . . . . 5
87r19.21bi 2833 . . . 4
94, 8sylbi 195 . . 3
103, 9sylbi 195 . 2
11 ssel 3498 . . . 4
12 bnj93 33217 . . . . 5
1312ex 434 . . . 4
1411, 13sylan9r 658 . . 3
1514ralrimiv 2876 . 2
1610, 15sylan2 474 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  wral 2814  cvv 3113   wss 3476  c0 3785  ciun 4325   csuc 4880  cfv 5588  com 6685   w-bnj17 33035   c-bnj14 33037   w-bnj15 33041 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686  ax-un 6577 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-pss 3492  df-nul 3786  df-if 3940  df-pw 4012  df-sn 4028  df-pr 4030  df-tp 4032  df-op 4034  df-uni 4246  df-iun 4327  df-br 4448  df-opab 4506  df-tr 4541  df-eprel 4791  df-po 4800  df-so 4801  df-fr 4838  df-we 4840  df-ord 4881  df-on 4882  df-lim 4883  df-suc 4884  df-iota 5551  df-fv 5596  df-om 6686  df-bnj17 33036  df-bnj14 33038  df-bnj13 33040  df-bnj15 33042 This theorem is referenced by:  bnj535  33244  bnj546  33250
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