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Theorem nfwe 4550
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 4535 . 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 4548 . . 3  |-  F/ x  R  Fr  A
52, 3nfso 4501 . . 3  |-  F/ x  R  Or  A
64, 5nfan 1846 . 2  |-  F/ x
( R  Fr  A  /\  R  Or  A
)
71, 6nfxfr 1579 1  |-  F/ x  R  We  A
Colors of variables: wff set class
Syntax hints:    /\ wa 359   F/wnf 1553   F/_wnfc 2558    Or wor 4494    Fr wfr 4530    We wwe 4532
This theorem is referenced by:  nfoi  7475  aomclem6  27125
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-3or 937  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-rex 2703  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  df-so 4496  df-fr 4533  df-we 4535
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