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Theorem nfso 4811
 Description: Bound-variable hypothesis builder for total orders. (Contributed by Stefan O'Rear, 20-Jan-2015.)
Hypotheses
Ref Expression
nfpo.r
nfpo.a
Assertion
Ref Expression
nfso

Proof of Theorem nfso
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-so 4806 . 2
2 nfpo.r . . . 4
3 nfpo.a . . . 4
42, 3nfpo 4810 . . 3
5 nfcv 2619 . . . . . . 7
6 nfcv 2619 . . . . . . 7
75, 2, 6nfbr 4496 . . . . . 6
8 nfv 1707 . . . . . 6
96, 2, 5nfbr 4496 . . . . . 6
107, 8, 9nf3or 1936 . . . . 5
113, 10nfral 2843 . . . 4
123, 11nfral 2843 . . 3
134, 12nfan 1928 . 2
141, 13nfxfr 1645 1
 Colors of variables: wff setvar class Syntax hints:  /\wa 369  \/w3o 972  F/wnf 1616  F/_wnfc 2605  A.wral 2807   class class class wbr 4452  Powpo 4803  Orwor 4804 This theorem is referenced by:  nfwe  4860 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-po 4805  df-so 4806
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