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

Theorem nfxp 4371
 Description: Bound-variable hypothesis builder for cross product. (Contributed by NM, 15-Sep-2003.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
nfxp.1
nfxp.2
Assertion
Ref Expression
nfxp

Proof of Theorem nfxp
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-xp 4351 . 2
2 nfxp.1 . . . . 5
32nfcri 2172 . . . 4
4 nfxp.2 . . . . 5
54nfcri 2172 . . . 4
63, 5nfan 1457 . . 3
76nfopab 3825 . 2
81, 7nfcxfr 2175 1
 Colors of variables: wff set class Syntax hints:   wa 97   wcel 1393  wnfc 2165  copab 3817   cxp 4343 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-opab 3819  df-xp 4351 This theorem is referenced by:  opeliunxp  4395  nfres  4614  mpt2mptsx  5823  dmmpt2ssx  5825  fmpt2x  5826
 Copyright terms: Public domain W3C validator