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Theorem cbvralf 2928
 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 1630 . . . 4
2 cbvralf.1 . . . . . 6
32nfcri 2568 . . . . 5
4 nfs1v 2184 . . . . 5
53, 4nfim 1833 . . . 4
6 eleq1 2498 . . . . 5
7 sbequ12 1945 . . . . 5
86, 7imbi12d 313 . . . 4
91, 5, 8cbval 1983 . . 3
10 cbvralf.2 . . . . . 6
1110nfcri 2568 . . . . 5
12 cbvralf.3 . . . . . 6
1312nfsb 2187 . . . . 5
1411, 13nfim 1833 . . . 4
15 nfv 1630 . . . 4
16 eleq1 2498 . . . . 5
17 sbequ 2113 . . . . . 6
18 cbvralf.4 . . . . . . 7
19 cbvralf.5 . . . . . . 7
2018, 19sbie 2151 . . . . . 6
2117, 20syl6bb 254 . . . . 5
2216, 21imbi12d 313 . . . 4
2314, 15, 22cbval 1983 . . 3
249, 23bitri 242 . 2
25 df-ral 2712 . 2
26 df-ral 2712 . 2
2724, 25, 263bitr4i 270 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wnf 1554  wsb 1659   wcel 1726  wnfc 2561  wral 2707 This theorem is referenced by:  cbvrexf  2929  cbvral  2930  reusv2lem4  4729  reusv2  4731  ffnfvf  5897  nnwof  10545  evth2f  27664  evthf  27676  stoweidlem14  27741  stoweidlem28  27755  stoweidlem59  27786 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712
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