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

Theorem cbvrabv 2618
Description: Rule to change the bound variable in a restricted class abstraction, using implicit substitution. (Contributed by NM, 26-May-1999.)
Hypothesis
Ref Expression
cbvrabv.1 (𝑥 = 𝑦 → (𝜑𝜓))
Assertion
Ref Expression
cbvrabv {𝑥𝐴𝜑} = {𝑦𝐴𝜓}
Distinct variable groups:   𝑥,𝑦,𝐴   𝜑,𝑦   𝜓,𝑥
Allowed substitution hints:   𝜑(𝑥)   𝜓(𝑦)

Proof of Theorem cbvrabv
StepHypRef Expression
1 nfcv 2228 . 2 𝑥𝐴
2 nfcv 2228 . 2 𝑦𝐴
3 nfv 1466 . 2 𝑦𝜑
4 nfv 1466 . 2 𝑥𝜓
5 cbvrabv.1 . 2 (𝑥 = 𝑦 → (𝜑𝜓))
61, 2, 3, 4, 5cbvrab 2617 1 {𝑥𝐴𝜑} = {𝑦𝐴𝜓}
Colors of variables: wff set class
Syntax hints:  wi 4  wb 103   = wceq 1289  {crab 2363
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rab 2368
This theorem is referenced by:  pwnss  3994  acexmidlemv  5650  genipv  7068  ltexpri  7172  sqne2sq  11433
  Copyright terms: Public domain W3C validator