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Theorem nfwe 4813
Description: Bound-variable hypothesis builder for well-orderings. (Contributed by Stefan O'Rear, 20-Jan-2015.) (Revised by Mario Carneiro, 14-Oct-2016.)
Hypotheses
Ref Expression
nffr.r  |-  F/_ x R
nffr.a  |-  F/_ x A
Assertion
Ref Expression
nfwe  |-  F/ x  R  We  A

Proof of Theorem nfwe
StepHypRef Expression
1 df-we 4798 . 2  |-  ( R  We  A  <->  ( R  Fr  A  /\  R  Or  A ) )
2 nffr.r . . . 4  |-  F/_ x R
3 nffr.a . . . 4  |-  F/_ x A
42, 3nffr 4811 . . 3  |-  F/ x  R  Fr  A
52, 3nfso 4764 . . 3  |-  F/ x  R  Or  A
64, 5nfan 2013 . 2  |-  F/ x
( R  Fr  A  /\  R  Or  A
)
71, 6nfxfr 1698 1  |-  F/ x  R  We  A
Colors of variables: wff setvar class
Syntax hints:    /\ wa 371   F/wnf 1669   F/_wnfc 2581    Or wor 4757    Fr wfr 4793    We wwe 4795
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3or 987  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-br 4406  df-po 4758  df-so 4759  df-fr 4796  df-we 4798
This theorem is referenced by:  nfoi  8034  aomclem6  35929
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