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

Theorem nfpo 4032
Description: Bound-variable hypothesis builder for partial orders. (Contributed by Stefan O'Rear, 20-Jan-2015.)
Hypotheses
Ref Expression
nfpo.r  F/_ R
nfpo.a  F/_
Assertion
Ref Expression
nfpo  F/  R  Po

Proof of Theorem nfpo
Dummy variables  a  b  c are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-po 4027 . 2  R  Po  a  b  c  a R a  a R b  b R c  a R c
2 nfpo.a . . 3  F/_
3 nfcv 2178 . . . . . . . 8  F/_ a
4 nfpo.r . . . . . . . 8  F/_ R
53, 4, 3nfbr 3802 . . . . . . 7  F/  a R a
65nfn 1548 . . . . . 6  F/  a R a
7 nfcv 2178 . . . . . . . . 9  F/_ b
83, 4, 7nfbr 3802 . . . . . . . 8  F/  a R b
9 nfcv 2178 . . . . . . . . 9  F/_ c
107, 4, 9nfbr 3802 . . . . . . . 8  F/  b R c
118, 10nfan 1457 . . . . . . 7  F/ a R b  b R c
123, 4, 9nfbr 3802 . . . . . . 7  F/  a R c
1311, 12nfim 1464 . . . . . 6  F/ a R b  b R c  a R c
146, 13nfan 1457 . . . . 5  F/  a R a  a R b  b R c  a R c
152, 14nfralxy 2357 . . . 4  F/ c  a R a  a R b  b R c  a R c
162, 15nfralxy 2357 . . 3  F/ b  c  a R a  a R b  b R c  a R c
172, 16nfralxy 2357 . 2  F/ a  b  c  a R a  a R b  b R c  a R c
181, 17nfxfr 1363 1  F/  R  Po
Colors of variables: wff set class
Syntax hints:   wn 3   wi 4   wa 97   F/wnf 1349   F/_wnfc 2165  wral 2303   class class class wbr 3758    Po wpo 4025
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-in1 544  ax-in2 545  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-3an 887  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2308  df-v 2556  df-un 2919  df-sn 3376  df-pr 3377  df-op 3379  df-br 3759  df-po 4027
This theorem is referenced by:  nfso  4033
  Copyright terms: Public domain W3C validator