Theorem nffr 4858

Description: Bound-variable hypothesis builder for well-founded relations. (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
nffr

Proof of Theorem nffr

Dummy variables are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-fr 4843	. 2
2		nfcv 2619	. . . . . 6
3		nffr.a	. . . . . 6
4	2, 3	nfss 3496	. . . . 5
5		nfv 1707	. . . . 5
6	4, 5	nfan 1928	. . . 4
7		nfcv 2619	. . . . . . . 8
8		nffr.r	. . . . . . . 8
9		nfcv 2619	. . . . . . . 8
10	7, 8, 9	nfbr 4496	. . . . . . 7
11	10	nfn 1901	. . . . . 6
12	2, 11	nfral 2843	. . . . 5
13	2, 12	nfrex 2920	. . . 4
14	6, 13	nfim 1920	. . 3
15	14	nfal 1947	. 2
16	1, 15	nfxfr 1645	1

Syntax hints:  -.wn 3  ->wi 4  /\wa 369  A.wal 1393  F/wnf 1616  F/_wnfc 2605  =/=wne 2652  A.wral 2807  E.wrex 2808  C_wss 3475  c0 3784   class class class wbr 4452  Frwfr 4840

This theorem is referenced by:  nfwe  4860

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-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-fr 4843