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Theorem nfso 4033
Description: Bound-variable hypothesis builder for total orders. (Contributed by Stefan O'Rear, 20-Jan-2015.)
Hypotheses
Ref Expression
nfpo.r  F/_ R
nfpo.a  F/_
Assertion
Ref Expression
nfso  F/  R  Or

Proof of Theorem nfso
Dummy variables  a  b  c are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-iso 4028 . 2  R  Or  R  Po  a  b  c  a R b  a R c  c R b
2 nfpo.r . . . 4  F/_ R
3 nfpo.a . . . 4  F/_
42, 3nfpo 4032 . . 3  F/  R  Po
5 nfcv 2178 . . . . . . . 8  F/_ a
6 nfcv 2178 . . . . . . . 8  F/_ b
75, 2, 6nfbr 3802 . . . . . . 7  F/  a R b
8 nfcv 2178 . . . . . . . . 9  F/_ c
95, 2, 8nfbr 3802 . . . . . . . 8  F/  a R c
108, 2, 6nfbr 3802 . . . . . . . 8  F/  c R b
119, 10nfor 1466 . . . . . . 7  F/ a R c  c R b
127, 11nfim 1464 . . . . . 6  F/ a R b  a R c  c R b
133, 12nfralxy 2357 . . . . 5  F/ c  a R b  a R c  c R b
143, 13nfralxy 2357 . . . 4  F/ b  c  a R b  a R c  c R b
153, 14nfralxy 2357 . . 3  F/ a  b  c 
a R b  a R c  c R b
164, 15nfan 1457 . 2  F/ R  Po  a  b  c 
a R b  a R c  c R b
171, 16nfxfr 1363 1  F/  R  Or
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wo 629   F/wnf 1349   F/_wnfc 2165  wral 2303   class class class wbr 3758    Po wpo 4025    Or wor 4026
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  df-iso 4028
This theorem is referenced by: (None)
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