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Theorem nfpo 4500
 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 4495 . 2
2 nfpo.a . . 3
3 nfcv 2571 . . . . . . . 8
4 nfpo.r . . . . . . . 8
53, 4, 3nfbr 4248 . . . . . . 7
65nfn 1811 . . . . . 6
7 nfcv 2571 . . . . . . . . 9
83, 4, 7nfbr 4248 . . . . . . . 8
9 nfcv 2571 . . . . . . . . 9
107, 4, 9nfbr 4248 . . . . . . . 8
118, 10nfan 1846 . . . . . . 7
123, 4, 9nfbr 4248 . . . . . . 7
1311, 12nfim 1832 . . . . . 6
146, 13nfan 1846 . . . . 5
152, 14nfral 2751 . . . 4
162, 15nfral 2751 . . 3
172, 16nfral 2751 . 2
181, 17nfxfr 1579 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 359  wnf 1553  wnfc 2558  wral 2697   class class class wbr 4204   wpo 4493 This theorem is referenced by:  nfso  4501 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-po 4495
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