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Theorem cbvral2v 2535
Description: Change bound variables of double restricted universal quantification, using implicit substitution. (Contributed by NM, 10-Aug-2004.)
Hypotheses
Ref Expression
cbvral2v.1
cbvral2v.2
Assertion
Ref Expression
cbvral2v
Distinct variable groups:   ,   ,   ,,   ,,   ,   ,   ,   ,   ,
Allowed substitution hints:   (,,)   (,,)   (,)   (,)

Proof of Theorem cbvral2v
StepHypRef Expression
1 cbvral2v.1 . . . 4
21ralbidv 2320 . . 3
32cbvralv 2527 . 2
4 cbvral2v.2 . . . 4
54cbvralv 2527 . . 3
65ralbii 2324 . 2
73, 6bitri 173 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wral 2300
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305
This theorem is referenced by:  cbvral3v  2537  fununi  4910
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