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Theorem bnj540 29263
 Description: Technical lemma for bnj852 29292. 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
bnj540.1
bnj540.2
bnj540.3
Assertion
Ref Expression
bnj540
Distinct variable groups:   ,   ,,,   ,   ,
Allowed substitution hints:   (,,)   (,)   (,)   (,)   (,,)

Proof of Theorem bnj540
StepHypRef Expression
1 bnj540.2 . 2
2 bnj540.1 . . . 4
32sbcbii 3216 . . 3
4 bnj540.3 . . . 4
54bnj538 29108 . . 3
6 sbcimg 3202 . . . . 5
74, 6ax-mp 8 . . . 4
87ralbii 2729 . . 3
93, 5, 83bitri 263 . 2
104bnj525 29106 . . . 4
11 fveq1 5727 . . . . . 6
12 fveq1 5727 . . . . . . 7
1312bnj1113 29156 . . . . . 6
1411, 13eqeq12d 2450 . . . . 5
154, 14sbcie 3195 . . . 4
1610, 15imbi12i 317 . . 3
1716ralbii 2729 . 2
181, 9, 173bitri 263 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  wral 2705  cvv 2956  wsbc 3161  ciun 4093   csuc 4583  com 4845  cfv 5454   c-bnj14 29052 This theorem is referenced by:  bnj580  29284  bnj607  29287 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-sbc 3162  df-in 3327  df-ss 3334  df-uni 4016  df-iun 4095  df-br 4213  df-iota 5418  df-fv 5462
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