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Theorem cbvreucsf 3200
Description: A more general version of cbvreuv 2837 that has no distinct variable rextrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.)
Hypotheses
Ref Expression
cbvralcsf.1  F/_
cbvralcsf.2  F/_
cbvralcsf.3  F/
cbvralcsf.4  F/
cbvralcsf.5
cbvralcsf.6
Assertion
Ref Expression
cbvreucsf

Proof of Theorem cbvreucsf
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1619 . . . 4  F/
2 nfcsb1v 3168 . . . . . 6  F/_
32nfcri 2483 . . . . 5  F/
4 nfs1v 2106 . . . . 5  F/
53, 4nfan 1824 . . . 4  F/
6 id 19 . . . . . 6
7 csbeq1a 3144 . . . . . 6
86, 7eleq12d 2421 . . . . 5
9 sbequ12 1919 . . . . 5
108, 9anbi12d 691 . . . 4
111, 5, 10cbveu 2224 . . 3
12 nfcv 2489 . . . . . . 7  F/_
13 cbvralcsf.1 . . . . . . 7  F/_
1412, 13nfcsb 3170 . . . . . 6  F/_
1514nfcri 2483 . . . . 5  F/
16 cbvralcsf.3 . . . . . 6  F/
1716nfsb 2109 . . . . 5  F/
1815, 17nfan 1824 . . . 4  F/
19 nfv 1619 . . . 4  F/
20 id 19 . . . . . 6
21 csbeq1 3139 . . . . . . 7
22 sbsbc 3050 . . . . . . . . 9  [.  ].
2322abbii 2465 . . . . . . . 8  [.  ].
24 cbvralcsf.2 . . . . . . . . . . . 12  F/_
2524nfcri 2483 . . . . . . . . . . 11  F/
26 cbvralcsf.5 . . . . . . . . . . . 12
2726eleq2d 2420 . . . . . . . . . . 11
2825, 27sbie 2038 . . . . . . . . . 10
2928bicomi 193 . . . . . . . . 9
3029abbi2i 2464 . . . . . . . 8
31 df-csb 3137 . . . . . . . 8  [.  ].
3223, 30, 313eqtr4ri 2384 . . . . . . 7
3321, 32syl6eq 2401 . . . . . 6
3420, 33eleq12d 2421 . . . . 5
35 sbequ 2060 . . . . . 6
36 cbvralcsf.4 . . . . . . 7  F/
37 cbvralcsf.6 . . . . . . 7
3836, 37sbie 2038 . . . . . 6
3935, 38syl6bb 252 . . . . 5
4034, 39anbi12d 691 . . . 4
4118, 19, 40cbveu 2224 . . 3
4211, 41bitri 240 . 2
43 df-reu 2621 . 2
44 df-reu 2621 . 2
4542, 43, 443bitr4i 268 1
Colors of variables: wff setvar class
Syntax hints:   wi 4   wb 176   wa 358   F/wnf 1544   wceq 1642  wsb 1648   wcel 1710  weu 2204  cab 2339   F/_wnfc 2476  wreu 2616   [.wsbc 3046  csb 3136
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-eu 2208  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-reu 2621  df-sbc 3047  df-csb 3137
This theorem is referenced by: (None)
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