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Theorem cbvral 2546
 Description: Rule used to change bound variables, using implicit substitution. (Contributed by NM, 31-Jul-2003.)
Hypotheses
Ref Expression
cbvral.1
cbvral.2
cbvral.3
Assertion
Ref Expression
cbvral
Distinct variable groups:   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvral
StepHypRef Expression
1 nfcv 2194 . 2
2 nfcv 2194 . 2
3 cbvral.1 . 2
4 cbvral.2 . 2
5 cbvral.3 . 2
61, 2, 3, 4, 5cbvralf 2544 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wnf 1365  wral 2323 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328 This theorem is referenced by:  cbvralv  2550  cbvralsv  2561  cbviin  3723  frind  4117  ralxpf  4510  eqfnfv2f  5297  ralrnmpt  5337  dff13f  5437  ofrfval2  5755  fmpt2x  5854  indstr  8632  bj-bdfindes  10461  bj-findes  10493
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