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Theorem bnj609 29225
 Description: Technical lemma for bnj852 29229. 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
bnj609.1
bnj609.2
bnj609.3
Assertion
Ref Expression
bnj609
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem bnj609
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj609.2 . 2
2 bnj609.3 . . 3
3 dfsbcq 3155 . . 3
4 fveq1 5719 . . . 4
54eqeq1d 2443 . . 3
6 bnj609.1 . . . . 5
76sbcbii 3208 . . . 4
8 vex 2951 . . . . 5
9 fveq1 5719 . . . . . 6
109eqeq1d 2443 . . . . 5
118, 10sbcie 3187 . . . 4
127, 11bitri 241 . . 3
132, 3, 5, 12vtoclb 3001 . 2
141, 13bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wceq 1652   wcel 1725  cvv 2948  wsbc 3153  c0 3620  cfv 5446   c-bnj14 28989 This theorem is referenced by:  bnj600  29227  bnj908  29239  bnj934  29243 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-v 2950  df-sbc 3154  df-uni 4008  df-br 4205  df-iota 5410  df-fv 5454
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