Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  cbvrexsv Structured version   Unicode version

Theorem cbvrexsv 2946
 Description: Change bound variable by using a substitution. (Contributed by NM, 2-Mar-2008.) (Revised by Andrew Salmon, 11-Jul-2011.)
Assertion
Ref Expression
cbvrexsv
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem cbvrexsv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1630 . . 3
2 nfs1v 2184 . . 3
3 sbequ12 1945 . . 3
41, 2, 3cbvrex 2931 . 2
5 nfv 1630 . . . 4
65nfsb 2187 . . 3
7 nfv 1630 . . 3
8 sbequ 2113 . . 3
96, 7, 8cbvrex 2931 . 2
104, 9bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178  wsb 1659  wrex 2708 This theorem is referenced by:  rspesbca  3243  ac6sf  8374  ac6gf  26448  cbvexsv  28707 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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  df-rex 2713
 Copyright terms: Public domain W3C validator