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Theorem bnj985 29772
 Description: Technical lemma for bnj69 29827. 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
bnj985.3
bnj985.6
bnj985.9
bnj985.11
bnj985.13
Assertion
Ref Expression
bnj985
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,)   (,,)   (,,)   (,,)   (,)   (,,)   (,,)

Proof of Theorem bnj985
StepHypRef Expression
1 bnj985.13 . . . 4
21bnj918 29585 . . 3
3 bnj985.3 . . . 4
4 bnj985.11 . . . 4
53, 4bnj984 29771 . . 3
62, 5ax-mp 5 . 2
7 sbcex2 3350 . . 3
8 nfv 1755 . . . . . . 7
98sb8e 2223 . . . . . 6
10 sbsbc 3303 . . . . . . 7
1110exbii 1712 . . . . . 6
129, 11bitri 252 . . . . 5
13 bnj985.6 . . . . 5
1412, 13bnj133 29541 . . . 4
1514sbcbii 3355 . . 3
16 bnj985.9 . . . 4
1716exbii 1712 . . 3
187, 15, 173bitr4i 280 . 2
196, 18bitri 252 1
 Colors of variables: wff setvar class Syntax hints:   wb 187   w3a 982   wceq 1437  wex 1657  wsb 1790   wcel 1872  cab 2407  wrex 2772  cvv 3080  wsbc 3299   cun 3434  csn 3998  cop 4004   wfn 5596   w-bnj17 29499 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-8 1874  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401  ax-sep 4546  ax-nul 4555  ax-pr 4660  ax-un 6597 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ne 2616  df-rex 2777  df-v 3082  df-sbc 3300  df-dif 3439  df-un 3441  df-nul 3762  df-sn 3999  df-pr 4001  df-uni 4220  df-bnj17 29500 This theorem is referenced by:  bnj1018  29781
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