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Theorem bnj546 29267
 Description: Technical lemma for bnj852 29292. 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
bnj546.1
bnj546.2
bnj546.3
bnj546.4
bnj546.5
Assertion
Ref Expression
bnj546
Distinct variable groups:   ,,,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj546
StepHypRef Expression
1 bnj546.2 . . . . . . 7
2 3simpc 956 . . . . . . 7
31, 2sylbi 188 . . . . . 6
4 bnj546.3 . . . . . . 7
5 bnj546.1 . . . . . . . . . 10
65bnj923 29137 . . . . . . . . 9
763ad2ant1 978 . . . . . . . 8
8 simp3 959 . . . . . . . 8
97, 8jca 519 . . . . . . 7
104, 9sylbi 188 . . . . . 6
113, 10anim12i 550 . . . . 5
12 bnj256 29070 . . . . 5
1311, 12sylibr 204 . . . 4
1413anim2i 553 . . 3
15143impb 1149 . 2
16 bnj546.4 . . 3
17 bnj546.5 . . 3
18 biid 228 . . 3
1916, 17, 18bnj518 29257 . 2
20 fvex 5742 . . 3
21 iunexg 5987 . . 3
2220, 21mpan 652 . 2
2315, 19, 223syl 19 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2705  cvv 2956   cdif 3317  c0 3628  csn 3814  ciun 4093   csuc 4583  com 4845   wfn 5449  cfv 5454   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056 This theorem is referenced by:  bnj938  29308 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-pr 4403  ax-un 4701 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-bnj17 29051  df-bnj14 29053  df-bnj13 29055  df-bnj15 29057
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