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Theorem bnj558 29273
 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
bnj558.3
bnj558.16
bnj558.17
bnj558.18
bnj558.19
bnj558.20
bnj558.21
bnj558.22
bnj558.23
bnj558.24
bnj558.25
bnj558.28
bnj558.29
bnj558.36
Assertion
Ref Expression
bnj558
Distinct variable groups:   ,,,   ,   ,,,   ,,,   ,,   ,
Allowed substitution hints:   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,,)   (,,,,,,)   (,,,,,,)   (,,,)   (,,,,,)   (,,,,,,)   (,,,,,,)   (,,,,,)   (,,,,,,)

Proof of Theorem bnj558
StepHypRef Expression
1 bnj558.3 . . 3
2 bnj558.16 . . 3
3 bnj558.17 . . 3
4 bnj558.18 . . 3
5 bnj558.19 . . 3
6 bnj558.20 . . 3
7 bnj558.21 . . 3
8 bnj558.22 . . 3
9 bnj558.23 . . 3
10 bnj558.24 . . 3
11 bnj558.25 . . 3
12 bnj558.28 . . 3
13 bnj558.29 . . 3
14 bnj558.36 . . 3
151, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14bnj557 29272 . 2
16 bnj422 29079 . . . . 5
17 bnj253 29068 . . . . 5
1816, 17bitri 241 . . . 4
1918simp1bi 972 . . 3
205, 6, 9, 10, 9, 10bnj554 29270 . . 3
2119, 20syl 16 . 2
2215, 21mpbid 202 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725  wral 2705   cdif 3317   cun 3318  c0 3628  csn 3814  cop 3817  ciun 4093   csuc 4583  com 4845   wfn 5449  cfv 5454   w-bnj17 29050   c-bnj14 29052   w-bnj15 29056 This theorem is referenced by:  bnj571  29277 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-sep 4330  ax-nul 4338  ax-pr 4403  ax-un 4701  ax-reg 7560 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  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-rab 2714  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-opab 4267  df-eprel 4494  df-id 4498  df-fr 4541  df-suc 4587  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-res 4890  df-iota 5418  df-fun 5456  df-fn 5457  df-fv 5462  df-bnj17 29051
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