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Theorem bnj611 29290
 Description: Technical lemma for bnj852 29293. 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 2711 . . . . 5
32bicomi 195 . . . 4
43sbcbii 3217 . . 3
5 bnj611.3 . . . . . . 7
6 nfv 1630 . . . . . . . 8
76sbc19.21g 3226 . . . . . . 7
85, 7ax-mp 8 . . . . . 6
9 nfv 1630 . . . . . . . . . 10
109sbc19.21g 3226 . . . . . . . . 9
115, 10ax-mp 8 . . . . . . . 8
12 fveq1 5728 . . . . . . . . . . 11
13 fveq1 5728 . . . . . . . . . . . 12
1413bnj1113 29157 . . . . . . . . . . 11
1512, 14eqeq12d 2451 . . . . . . . . . 10
16 fveq1 5728 . . . . . . . . . . 11
17 fveq1 5728 . . . . . . . . . . . 12
1817bnj1113 29157 . . . . . . . . . . 11
1916, 18eqeq12d 2451 . . . . . . . . . 10
20 fveq1 5728 . . . . . . . . . . 11
21 fveq1 5728 . . . . . . . . . . . 12
2221bnj1113 29157 . . . . . . . . . . 11
2320, 22eqeq12d 2451 . . . . . . . . . 10
245, 15, 19, 23bnj610 29116 . . . . . . . . 9
2524imbi2i 305 . . . . . . . 8
2611, 25bitri 242 . . . . . . 7
2726imbi2i 305 . . . . . 6
288, 27bitri 242 . . . . 5
2928albii 1576 . . . 4
30 sbcal 3209 . . . 4
31 df-ral 2711 . . . 4
3229, 30, 313bitr4ri 271 . . 3
33 bnj611.1 . . . 4
3433sbcbii 3217 . . 3
354, 32, 343bitr4ri 271 . 2
361, 35bitri 242 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550   wceq 1653   wcel 1726  wral 2706  cvv 2957  wsbc 3162  ciun 4094   csuc 4584  com 4846  cfv 5455   c-bnj14 29053 This theorem is referenced by:  bnj600  29291  bnj908  29303 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-v 2959  df-sbc 3163  df-in 3328  df-ss 3335  df-uni 4017  df-iun 4096  df-br 4214  df-iota 5419  df-fv 5463
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