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Theorem nfso 4336
 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 4331 . 2
2 nfpo.r . . . 4
3 nfpo.a . . . 4
42, 3nfpo 4335 . . 3
5 nfcv 2432 . . . . . . 7
6 nfcv 2432 . . . . . . 7
75, 2, 6nfbr 4083 . . . . . 6
8 nfv 1609 . . . . . 6
96, 2, 5nfbr 4083 . . . . . 6
107, 8, 9nf3or 1785 . . . . 5
113, 10nfral 2609 . . . 4
123, 11nfral 2609 . . 3
134, 12nfan 1783 . 2
141, 13nfxfr 1560 1
 Colors of variables: wff set class Syntax hints:   wa 358   w3o 933  wnf 1534   wceq 1632  wnfc 2419  wral 2556   class class class wbr 4039   wpo 4328   wor 4329 This theorem is referenced by:  nfwe  4385 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-br 4040  df-po 4330  df-so 4331
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