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Theorem nfso 4777
 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 4772 . 2
2 nfpo.r . . . 4
3 nfpo.a . . . 4
42, 3nfpo 4776 . . 3
5 nfcv 2584 . . . . . . 7
6 nfcv 2584 . . . . . . 7
75, 2, 6nfbr 4465 . . . . . 6
8 nfv 1751 . . . . . 6
96, 2, 5nfbr 4465 . . . . . 6
107, 8, 9nf3or 1992 . . . . 5
113, 10nfral 2811 . . . 4
123, 11nfral 2811 . . 3
134, 12nfan 1984 . 2
141, 13nfxfr 1692 1
 Colors of variables: wff setvar class Syntax hints:   wa 370   w3o 981  wnf 1663  wnfc 2570  wral 2775   class class class wbr 4420   wpo 4769   wor 4770 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3or 983  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ral 2780  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-br 4421  df-po 4771  df-so 4772 This theorem is referenced by:  nfwe  4826
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