Theorem nfso 4811

Description: Bound-variable hypothesis builder for total orders. (Contributed by Stefan O'Rear, 20-Jan-2015.)

Hypotheses

Ref	Expression
nfpo.r
nfpo.a

Assertion

Ref	Expression
nfso

Proof of Theorem nfso

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

Step	Hyp	Ref	Expression
1		df-so 4806	. 2
2		nfpo.r	. . . 4
3		nfpo.a	. . . 4
4	2, 3	nfpo 4810	. . 3
5		nfcv 2619	. . . . . . 7
6		nfcv 2619	. . . . . . 7
7	5, 2, 6	nfbr 4496	. . . . . 6
8		nfv 1707	. . . . . 6
9	6, 2, 5	nfbr 4496	. . . . . 6
10	7, 8, 9	nf3or 1936	. . . . 5
11	3, 10	nfral 2843	. . . 4
12	3, 11	nfral 2843	. . 3
13	4, 12	nfan 1928	. 2
14	1, 13	nfxfr 1645	1

Syntax hints:  /\wa 369  \/w3o 972  F/wnf 1616  F/_wnfc 2605  A.wral 2807   class class class wbr 4452  Powpo 4803  Orwor 4804

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-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-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