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Theorem nfpo 4066
 Description: Bound-variable hypothesis builder for partial orders. (Contributed by Stefan O'Rear, 20-Jan-2015.)
Hypotheses
Ref Expression
nfpo.r
nfpo.a
Assertion
Ref Expression
nfpo

Proof of Theorem nfpo
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-po 4061 . 2
2 nfpo.a . . 3
3 nfcv 2194 . . . . . . . 8
4 nfpo.r . . . . . . . 8
53, 4, 3nfbr 3836 . . . . . . 7
65nfn 1564 . . . . . 6
7 nfcv 2194 . . . . . . . . 9
83, 4, 7nfbr 3836 . . . . . . . 8
9 nfcv 2194 . . . . . . . . 9
107, 4, 9nfbr 3836 . . . . . . . 8
118, 10nfan 1473 . . . . . . 7
123, 4, 9nfbr 3836 . . . . . . 7
1311, 12nfim 1480 . . . . . 6
146, 13nfan 1473 . . . . 5
152, 14nfralxy 2377 . . . 4
162, 15nfralxy 2377 . . 3
172, 16nfralxy 2377 . 2
181, 17nfxfr 1379 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 101  wnf 1365  wnfc 2181  wral 2323   class class class wbr 3792   wpo 4059 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-fal 1265  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-br 3793  df-po 4061 This theorem is referenced by:  nfso  4067
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