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Theorem bnj1190 29817
 Description: Technical lemma for bnj69 29819. 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
bnj1190.1
bnj1190.2
Assertion
Ref Expression
bnj1190
Distinct variable groups:   ,,,   ,,,   ,,,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1190
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1190.1 . . . . . . 7
21simp2bi 1024 . . . . . 6
32adantr 467 . . . . 5
4 eqid 2451 . . . . . 6
5 bnj1190.2 . . . . . . . . 9
61simp1bi 1023 . . . . . . . . . 10
76adantr 467 . . . . . . . . 9
85simp1bi 1023 . . . . . . . . . 10
9 ssel2 3427 . . . . . . . . . 10
102, 8, 9syl2an 480 . . . . . . . . 9
115, 4, 7, 3, 10bnj1177 29815 . . . . . . . 8
12 bnj1154 29808 . . . . . . . 8
1311, 12bnj1176 29814 . . . . . . 7
14 biid 240 . . . . . . . 8
15 biid 240 . . . . . . . 8
164, 14, 15bnj1175 29813 . . . . . . 7
174, 13, 16bnj1174 29812 . . . . . 6
184, 15, 7, 10bnj1173 29811 . . . . . 6
194, 17, 18bnj1172 29810 . . . . 5
203, 19bnj1171 29809 . . . 4
2120bnj1186 29816 . . 3
2221bnj1185 29605 . 2
2322bnj1185 29605 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371   w3a 985   wcel 1887   wne 2622  wral 2737  wrex 2738   cin 3403   wss 3404  c0 3731   class class class wbr 4402   w-bnj15 29497   c-bnj18 29499 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-8 1889  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-rep 4515  ax-sep 4525  ax-nul 4534  ax-pow 4581  ax-pr 4639  ax-un 6583  ax-reg 8107  ax-inf2 8146 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 986  df-3an 987  df-tru 1447  df-fal 1450  df-ex 1664  df-nf 1668  df-sb 1798  df-eu 2303  df-mo 2304  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-ral 2742  df-rex 2743  df-reu 2744  df-rab 2746  df-v 3047  df-sbc 3268  df-csb 3364  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-pss 3420  df-nul 3732  df-if 3882  df-pw 3953  df-sn 3969  df-pr 3971  df-tp 3973  df-op 3975  df-uni 4199  df-iun 4280  df-br 4403  df-opab 4462  df-mpt 4463  df-tr 4498  df-eprel 4745  df-id 4749  df-po 4755  df-so 4756  df-fr 4793  df-we 4795  df-xp 4840  df-rel 4841  df-cnv 4842  df-co 4843  df-dm 4844  df-rn 4845  df-res 4846  df-ima 4847  df-ord 5426  df-on 5427  df-lim 5428  df-suc 5429  df-iota 5546  df-fun 5584  df-fn 5585  df-f 5586  df-f1 5587  df-fo 5588  df-f1o 5589  df-fv 5590  df-om 6693  df-1o 7182  df-bnj17 29492  df-bnj14 29494  df-bnj13 29496  df-bnj15 29498  df-bnj18 29500  df-bnj19 29502 This theorem is referenced by:  bnj1189  29818
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