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

Theorem nfcsb 2857
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 1331 . . 3 y
2 nfcsb.1 . . . 4 xA
32a1i 9 . . 3 ( ⊤ → xA)
4 nfcsb.2 . . . 4 xB
54a1i 9 . . 3 ( ⊤ → xB)
61, 3, 5nfcsbd 2856 . 2 ( ⊤ → xA / yB)
76trud 1235 1 xA / yB
Colors of variables: wff set class
Syntax hints:  wtru 1227  wnfc 2143  csb 2825
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 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-sbc 2738  df-csb 2826
This theorem is referenced by:  cbvralcsf  2881  cbvrexcsf  2882  cbvreucsf  2883  cbvrabcsf  2884  fmptcof  5252  mpt2mptsx  5742  dmmpt2ssx  5744  fmpt2x  5745  fmpt2co  5756  dfmpt2  5763
  Copyright terms: Public domain W3C validator