Theorem nfwe 4860

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
nffr.a

Assertion

Ref	Expression
nfwe

Proof of Theorem nfwe

Step	Hyp	Ref	Expression
1		df-we 4845	. 2
2		nffr.r	. . . 4
3		nffr.a	. . . 4
4	2, 3	nffr 4858	. . 3
5	2, 3	nfso 4811	. . 3
6	4, 5	nfan 1928	. 2
7	1, 6	nfxfr 1645	1

Syntax hints:  /\wa 369  F/wnf 1616  F/_wnfc 2605  Orwor 4804  Frwfr 4840  Wewwe 4842

This theorem is referenced by:  nfoi  7960  aomclem6  31005

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435

This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3or 974  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-po 4805  df-so 4806  df-fr 4843  df-we 4845