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Theorem cbvralsv 2663
 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 1508 . . 3
2 nfs1v 1910 . . 3
3 sbequ12 1744 . . 3
41, 2, 3cbvral 2648 . 2
5 nfv 1508 . . . 4
65nfsb 1917 . . 3
7 nfv 1508 . . 3
8 sbequ 1812 . . 3
96, 7, 8cbvral 2648 . 2
104, 9bitri 183 1
 Colors of variables: wff set class Syntax hints:   wb 104  wsb 1735  wral 2414 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-cleq 2130  df-clel 2133  df-nfc 2268  df-ral 2419 This theorem is referenced by:  sbralie  2665  rspsbc  2986  ralxpf  4680
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