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

Theorem nfcsb 2966
Description: Bound-variable hypothesis builder for substitution into a class. (Contributed by Mario Carneiro, 12-Oct-2016.)
Hypotheses
Ref Expression
nfcsb.1 𝑥𝐴
nfcsb.2 𝑥𝐵
Assertion
Ref Expression
nfcsb 𝑥𝐴 / 𝑦𝐵

Proof of Theorem nfcsb
StepHypRef Expression
1 nftru 1401 . . 3 𝑦
2 nfcsb.1 . . . 4 𝑥𝐴
32a1i 9 . . 3 (⊤ → 𝑥𝐴)
4 nfcsb.2 . . . 4 𝑥𝐵
54a1i 9 . . 3 (⊤ → 𝑥𝐵)
61, 3, 5nfcsbd 2965 . 2 (⊤ → 𝑥𝐴 / 𝑦𝐵)
76mptru 1299 1 𝑥𝐴 / 𝑦𝐵
Colors of variables: wff set class
Syntax hints:  wtru 1291  wnfc 2216  csb 2934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-sbc 2842  df-csb 2935
This theorem is referenced by:  cbvralcsf  2991  cbvrexcsf  2992  cbvreucsf  2993  cbvrabcsf  2994  fmptcof  5479  mpt2mptsx  5981  dmmpt2ssx  5983  fmpt2x  5984  fmpt2co  5995  dfmpt2  6002  f1od2  6014  nfsum  10807  fsum2dlemstep  10889  fisumcom2  10893
  Copyright terms: Public domain W3C validator