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Theorem cbvrexf 2522
Description: Rule used to change bound variables, using implicit substitution. (Contributed by FL, 27-Apr-2008.) (Revised by Mario Carneiro, 9-Oct-2016.) (Proof rewritten by Jim Kingdon, 10-Jun-2018.)
Hypotheses
Ref Expression
cbvralf.1  F/_
cbvralf.2  F/_
cbvralf.3  F/
cbvralf.4  F/
cbvralf.5
Assertion
Ref Expression
cbvrexf

Proof of Theorem cbvrexf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1418 . . . 4  F/
2 cbvralf.1 . . . . . 6  F/_
32nfcri 2169 . . . . 5  F/
4 nfs1v 1812 . . . . 5  F/
53, 4nfan 1454 . . . 4  F/
6 eleq1 2097 . . . . 5
7 sbequ12 1651 . . . . 5
86, 7anbi12d 442 . . . 4
91, 5, 8cbvex 1636 . . 3
10 cbvralf.2 . . . . . 6  F/_
1110nfcri 2169 . . . . 5  F/
12 cbvralf.3 . . . . . 6  F/
1312nfsb 1819 . . . . 5  F/
1411, 13nfan 1454 . . . 4  F/
15 nfv 1418 . . . 4  F/
16 eleq1 2097 . . . . 5
17 sbequ 1718 . . . . . 6
18 cbvralf.4 . . . . . . 7  F/
19 cbvralf.5 . . . . . . 7
2018, 19sbie 1671 . . . . . 6
2117, 20syl6bb 185 . . . . 5
2216, 21anbi12d 442 . . . 4
2314, 15, 22cbvex 1636 . . 3
249, 23bitri 173 . 2
25 df-rex 2306 . 2
26 df-rex 2306 . 2
2724, 25, 263bitr4i 201 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   F/wnf 1346  wex 1378   wcel 1390  wsb 1642   F/_wnfc 2162  wrex 2301
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306
This theorem is referenced by:  cbvrex  2524
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