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Theorem cbvralsv 2943
 Description: Change bound variable by using a substitution. (Contributed by NM, 20-Nov-2005.) (Revised by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
cbvralsv
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem cbvralsv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1629 . . 3
2 nfs1v 2182 . . 3
3 sbequ12 1944 . . 3
41, 2, 3cbvral 2928 . 2
5 nfv 1629 . . . 4
65nfsb 2185 . . 3
7 nfv 1629 . . 3
8 sbequ 2111 . . 3
96, 7, 8cbvral 2928 . 2
104, 9bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177  wsb 1658  wral 2705 This theorem is referenced by:  sbralie  2945  rspsbc  3239  tfinds  4839  tfindes  4842  ralxpf  5019 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 2417 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 2429  df-clel 2432  df-nfc 2561  df-ral 2710
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