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Theorem cbvrabcsf 3469
Description: A more general version of cbvrab 3107 with no distinct variable restrictions. (Contributed by Andrew Salmon, 13-Jul-2011.)
Hypotheses
Ref Expression
cbvralcsf.1
cbvralcsf.2
cbvralcsf.3
cbvralcsf.4
cbvralcsf.5
cbvralcsf.6
Assertion
Ref Expression
cbvrabcsf

Proof of Theorem cbvrabcsf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1707 . . . 4
2 nfcsb1v 3450 . . . . . 6
32nfcri 2612 . . . . 5
4 nfs1v 2181 . . . . 5
53, 4nfan 1928 . . . 4
6 id 22 . . . . . 6
7 csbeq1a 3443 . . . . . 6
86, 7eleq12d 2539 . . . . 5
9 sbequ12 1992 . . . . 5
108, 9anbi12d 710 . . . 4
111, 5, 10cbvab 2598 . . 3
12 nfcv 2619 . . . . . . 7
13 cbvralcsf.1 . . . . . . 7
1412, 13nfcsb 3452 . . . . . 6
1514nfcri 2612 . . . . 5
16 cbvralcsf.3 . . . . . 6
1716nfsb 2184 . . . . 5
1815, 17nfan 1928 . . . 4
19 nfv 1707 . . . 4
20 id 22 . . . . . 6
21 csbeq1 3437 . . . . . . 7
22 df-csb 3435 . . . . . . . 8
23 cbvralcsf.2 . . . . . . . . . . . 12
2423nfcri 2612 . . . . . . . . . . 11
25 cbvralcsf.5 . . . . . . . . . . . 12
2625eleq2d 2527 . . . . . . . . . . 11
2724, 26sbie 2149 . . . . . . . . . 10
28 sbsbc 3331 . . . . . . . . . 10
2927, 28bitr3i 251 . . . . . . . . 9
3029abbi2i 2590 . . . . . . . 8
3122, 30eqtr4i 2489 . . . . . . 7
3221, 31syl6eq 2514 . . . . . 6
3320, 32eleq12d 2539 . . . . 5
34 sbequ 2117 . . . . . 6
35 cbvralcsf.4 . . . . . . 7
36 cbvralcsf.6 . . . . . . 7
3735, 36sbie 2149 . . . . . 6
3834, 37syl6bb 261 . . . . 5
3933, 38anbi12d 710 . . . 4
4018, 19, 39cbvab 2598 . . 3
4111, 40eqtri 2486 . 2
42 df-rab 2816 . 2
43 df-rab 2816 . 2
4441, 42, 433eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  [wsb 1739  e.wcel 1818  {cab 2442  F/_wnfc 2605  {crab 2811  [.wsbc 3327  [_csb 3434
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-sbc 3328  df-csb 3435
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