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Theorem bnj1173 29308
 Description: Technical lemma for bnj69 29316. 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
bnj1173.3
bnj1173.5
bnj1173.9
bnj1173.17
Assertion
Ref Expression
bnj1173

Proof of Theorem bnj1173
StepHypRef Expression
1 bnj1173.5 . . 3
2 3simpc 956 . . . 4
3 bnj1173.9 . . . . . . 7
433adant3 977 . . . . . 6
5 bnj1173.17 . . . . . . 7
653adant3 977 . . . . . 6
7 elin 3522 . . . . . . . . 9
87simplbi 447 . . . . . . . 8
9 bnj1173.3 . . . . . . . 8
108, 9eleq2s 2527 . . . . . . 7
11103ad2ant3 980 . . . . . 6
12 pm3.21 436 . . . . . 6
134, 6, 11, 12syl3anc 1184 . . . . 5
14 bnj170 28999 . . . . 5
1513, 14syl6ibr 219 . . . 4
162, 15impbid2 196 . . 3
171, 16syl5bb 249 . 2
18 bnj1147 29300 . . . . 5
1918, 11bnj1213 29107 . . . 4
204, 19jca 519 . . 3
2120biantrurd 495 . 2
2217, 21bitr4d 248 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936   wceq 1652   wcel 1725   cin 3311   w-bnj15 28993   c-bnj18 28995 This theorem is referenced by:  bnj1190  29314 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-sep 4322  ax-nul 4330  ax-pr 4395  ax-un 4693 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-rab 2706  df-v 2950  df-sbc 3154  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-tr 4295  df-eprel 4486  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-iota 5410  df-fn 5449  df-fv 5454  df-bnj17 28988  df-bnj14 28990  df-bnj18 28996
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