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Theorem cbvralf 2918
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 1629 . . . 4
2 cbvralf.1 . . . . . 6
32nfcri 2565 . . . . 5
4 nfs1v 2181 . . . . 5
53, 4nfim 1832 . . . 4
6 eleq1 2495 . . . . 5
7 sbequ12 1944 . . . . 5
86, 7imbi12d 312 . . . 4
91, 5, 8cbval 1982 . . 3
10 cbvralf.2 . . . . . 6
1110nfcri 2565 . . . . 5
12 cbvralf.3 . . . . . 6
1312nfsb 2184 . . . . 5
1411, 13nfim 1832 . . . 4
15 nfv 1629 . . . 4
16 eleq1 2495 . . . . 5
17 sbequ 2138 . . . . . 6
18 cbvralf.4 . . . . . . 7
19 cbvralf.5 . . . . . . 7
2018, 19sbie 2122 . . . . . 6
2117, 20syl6bb 253 . . . . 5
2216, 21imbi12d 312 . . . 4
2314, 15, 22cbval 1982 . . 3
249, 23bitri 241 . 2
25 df-ral 2702 . 2
26 df-ral 2702 . 2
2724, 25, 263bitr4i 269 1
Colors of variables: wff set class
Syntax hints:  ->wi 4  <->wb 177  A.wal 1549  F/wnf 1553  [wsb 1658  e.wcel 1725  F/_wnfc 2558  A.wral 2697
This theorem is referenced by:  cbvrexf  2919  cbvral  2920  reusv2lem4  4719  reusv2  4721  ffnfvf  5887  nnwof  10535  evth2f  27653  evthf  27665  stoweidlem14  27730  stoweidlem28  27744  stoweidlem59  27775
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702
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