Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  cbvrab Unicode version

Theorem cbvrab 2572
 Description: Rule to change the bound variable in a restricted class abstraction, using implicit substitution. This version has bound-variable hypotheses in place of distinct variable conditions. (Contributed by Andrew Salmon, 11-Jul-2011.) (Revised by Mario Carneiro, 9-Oct-2016.)
Hypotheses
Ref Expression
cbvrab.1
cbvrab.2
cbvrab.3
cbvrab.4
cbvrab.5
Assertion
Ref Expression
cbvrab

Proof of Theorem cbvrab
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1437 . . . 4
2 cbvrab.1 . . . . . 6
32nfcri 2188 . . . . 5
4 nfs1v 1831 . . . . 5
53, 4nfan 1473 . . . 4
6 eleq1 2116 . . . . 5
7 sbequ12 1670 . . . . 5
86, 7anbi12d 450 . . . 4
91, 5, 8cbvab 2176 . . 3
10 cbvrab.2 . . . . . 6
1110nfcri 2188 . . . . 5
12 cbvrab.3 . . . . . 6
1312nfsb 1838 . . . . 5
1411, 13nfan 1473 . . . 4
15 nfv 1437 . . . 4
16 eleq1 2116 . . . . 5
17 sbequ 1737 . . . . . 6
18 cbvrab.4 . . . . . . 7
19 cbvrab.5 . . . . . . 7
2018, 19sbie 1690 . . . . . 6
2117, 20syl6bb 189 . . . . 5
2216, 21anbi12d 450 . . . 4
2314, 15, 22cbvab 2176 . . 3
249, 23eqtri 2076 . 2
25 df-rab 2332 . 2
26 df-rab 2332 . 2
2724, 25, 263eqtr4i 2086 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 101   wb 102   wceq 1259  wnf 1365   wcel 1409  wsb 1661  cab 2042  wnfc 2181  crab 2327 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-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-rab 2332 This theorem is referenced by:  cbvrabv  2573  elrabsf  2824  tfis  4334
 Copyright terms: Public domain W3C validator