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Theorem bnj611 29303
 Description: Technical lemma for bnj852 29306. 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
bnj611.1
bnj611.2
bnj611.3
Assertion
Ref Expression
bnj611
Distinct variable groups:   ,   ,,   ,   ,   ,,
Allowed substitution hints:   (,,)   (,)   (,)   ()   (,)   (,,)

Proof of Theorem bnj611
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj611.2 . 2
2 df-ral 2759 . . . . 5
32bicomi 202 . . . 4
43sbcbii 3333 . . 3
5 bnj611.3 . . . . . . 7
6 nfv 1728 . . . . . . . 8
76sbc19.21g 3342 . . . . . . 7
85, 7ax-mp 5 . . . . . 6
9 nfv 1728 . . . . . . . . . 10
109sbc19.21g 3342 . . . . . . . . 9
115, 10ax-mp 5 . . . . . . . 8
12 fveq1 5848 . . . . . . . . . . 11
13 fveq1 5848 . . . . . . . . . . . 12
1413bnj1113 29171 . . . . . . . . . . 11
1512, 14eqeq12d 2424 . . . . . . . . . 10
16 fveq1 5848 . . . . . . . . . . 11
17 fveq1 5848 . . . . . . . . . . . 12
1817bnj1113 29171 . . . . . . . . . . 11
1916, 18eqeq12d 2424 . . . . . . . . . 10
20 fveq1 5848 . . . . . . . . . . 11
21 fveq1 5848 . . . . . . . . . . . 12
2221bnj1113 29171 . . . . . . . . . . 11
2320, 22eqeq12d 2424 . . . . . . . . . 10
245, 15, 19, 23bnj610 29131 . . . . . . . . 9
2524imbi2i 310 . . . . . . . 8
2611, 25bitri 249 . . . . . . 7
2726imbi2i 310 . . . . . 6
288, 27bitri 249 . . . . 5
2928albii 1661 . . . 4
30 sbcal 3327 . . . 4
31 df-ral 2759 . . . 4
3229, 30, 313bitr4ri 278 . . 3
33 bnj611.1 . . . 4
3433sbcbii 3333 . . 3
354, 32, 343bitr4ri 278 . 2
361, 35bitri 249 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184  wal 1403   wceq 1405   wcel 1842  wral 2754  cvv 3059  wsbc 3277  ciun 4271   csuc 5412  cfv 5569  com 6683   c-bnj14 29067 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ral 2759  df-rex 2760  df-v 3061  df-sbc 3278  df-in 3421  df-ss 3428  df-uni 4192  df-iun 4273  df-br 4396  df-iota 5533  df-fv 5577 This theorem is referenced by:  bnj600  29304  bnj908  29316
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