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Theorem bnj1374 29912
 Description: Technical lemma for bnj60 29943. 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
bnj1374.1
bnj1374.2
bnj1374.3
bnj1374.4
bnj1374.5
bnj1374.6
bnj1374.7
bnj1374.8
bnj1374.9
Assertion
Ref Expression
bnj1374
Distinct variable groups:   ,   ,   ,   ,   ,,   ,,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,)   (,,)   (,,)   (,,,)   (,,)   (,,,)   (,,,)   (,,,)   (,,,)

Proof of Theorem bnj1374
StepHypRef Expression
1 bnj1374.9 . . . . . 6
21bnj1436 29723 . . . . 5
3 rexex 2843 . . . . 5
42, 3syl 17 . . . 4
5 bnj1374.1 . . . . . 6
6 bnj1374.2 . . . . . 6
7 bnj1374.3 . . . . . 6
8 bnj1374.4 . . . . . 6
9 bnj1374.8 . . . . . 6
105, 6, 7, 8, 9bnj1373 29911 . . . . 5
1110exbii 1726 . . . 4
124, 11sylib 201 . . 3
13 exsimpl 1737 . . 3
1412, 13syl 17 . 2
1514bnj937 29655 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376   w3a 1007   wceq 1452  wex 1671   wcel 1904  cab 2457   wne 2641  wral 2756  wrex 2757  crab 2760  wsbc 3255   cun 3388   wss 3390  c0 3722  csn 3959  cop 3965   class class class wbr 4395   cdm 4839   cres 4841   wfn 5584  cfv 5589   c-bnj14 29565   w-bnj15 29569   c-bnj18 29571 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-iun 4271  df-br 4396  df-bnj14 29566  df-bnj18 29572 This theorem is referenced by:  bnj1384  29913
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