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Theorem cbvralf 2527
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 7-Mar-2004.) (Revised by Mario Carneiro, 9-Oct-2016.)
Hypotheses
Ref Expression
cbvralf.1
cbvralf.2
cbvralf.3
cbvralf.4
cbvralf.5
Assertion
Ref Expression
cbvralf

Proof of Theorem cbvralf
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1421 . . . 4
2 cbvralf.1 . . . . . 6
32nfcri 2172 . . . . 5
4 nfs1v 1815 . . . . 5
53, 4nfim 1464 . . . 4
6 eleq1 2100 . . . . 5
7 sbequ12 1654 . . . . 5
86, 7imbi12d 223 . . . 4
91, 5, 8cbval 1637 . . 3
10 cbvralf.2 . . . . . 6
1110nfcri 2172 . . . . 5
12 cbvralf.3 . . . . . 6
1312nfsb 1822 . . . . 5
1411, 13nfim 1464 . . . 4
15 nfv 1421 . . . 4
16 eleq1 2100 . . . . 5
17 sbequ 1721 . . . . . 6
18 cbvralf.4 . . . . . . 7
19 cbvralf.5 . . . . . . 7
2018, 19sbie 1674 . . . . . 6
2117, 20syl6bb 185 . . . . 5
2216, 21imbi12d 223 . . . 4
2314, 15, 22cbval 1637 . . 3
249, 23bitri 173 . 2
25 df-ral 2311 . 2
26 df-ral 2311 . 2
2724, 25, 263bitr4i 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98  wal 1241  wnf 1349   wcel 1393  wsb 1645  wnfc 2165  wral 2306 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311 This theorem is referenced by:  cbvral  2529  ffnfvf  5324
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