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Theorem cbvralsv 3095
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:   ,   ,   ,

Proof of Theorem cbvralsv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1707 . . 3
2 nfs1v 2181 . . 3
3 sbequ12 1992 . . 3
41, 2, 3cbvral 3080 . 2
5 nfv 1707 . . . 4
65nfsb 2184 . . 3
7 nfv 1707 . . 3
8 sbequ 2117 . . 3
96, 7, 8cbvral 3080 . 2
104, 9bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  [wsb 1739  A.wral 2807
This theorem is referenced by:  sbralie  3097  rspsbc  3417  ralxpf  5154  tfinds  6694  tfindes  6697  nn0min  27611
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1613  df-nf 1617  df-sb 1740  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812
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