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Theorem bnj1190 29304
 Description: Technical lemma for bnj69 29306. 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 973 . . . . . 6
32adantr 452 . . . . 5
4 eqid 2435 . . . . . 6
5 bnj1190.2 . . . . . . . . 9
61simp1bi 972 . . . . . . . . . 10
76adantr 452 . . . . . . . . 9
85simp1bi 972 . . . . . . . . . 10
9 ssel2 3335 . . . . . . . . . 10
102, 8, 9syl2an 464 . . . . . . . . 9
115, 4, 7, 3, 10bnj1177 29302 . . . . . . . 8
12 bnj1154 29295 . . . . . . . 8
1311, 12bnj1176 29301 . . . . . . 7
14 biid 228 . . . . . . . 8
15 biid 228 . . . . . . . 8
164, 14, 15bnj1175 29300 . . . . . . 7
174, 13, 16bnj1174 29299 . . . . . 6
184, 15, 7, 10bnj1173 29298 . . . . . 6
194, 17, 18bnj1172 29297 . . . . 5
203, 19bnj1171 29296 . . . 4
2120bnj1186 29303 . . 3
2221bnj1185 29092 . 2
2322bnj1185 29092 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936   wcel 1725   wne 2598  wral 2697  wrex 2698   cin 3311   wss 3312  c0 3620   class class class wbr 4204   w-bnj15 28983   c-bnj18 28985 This theorem is referenced by:  bnj1189  29305 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 7552  ax-inf2 7588 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 28978  df-bnj14 28980  df-bnj13 28982  df-bnj15 28984  df-bnj18 28986  df-bnj19 28988
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