Theorem nfrmo 3033

Description: Bound-variable hypothesis builder for restricted uniqueness. (Contributed by NM, 16-Jun-2017.)

Hypotheses

Ref	Expression
nfreu.1
nfreu.2

Assertion

Ref	Expression
nfrmo

Proof of Theorem nfrmo

Step	Hyp	Ref	Expression
1		df-rmo 2815	. 2
2		nftru 1626	. . . 4
3		nfcvf 2644	. . . . . . 7
4		nfreu.1	. . . . . . . 8
5	4	a1i 11	. . . . . . 7
6	3, 5	nfeld 2627	. . . . . 6
7		nfreu.2	. . . . . . 7
8	7	a1i 11	. . . . . 6
9	6, 8	nfand 1925	. . . . 5
10	9	adantl 466	. . . 4
11	2, 10	nfmod2 2297	. . 3
12	11	trud 1404	. 2
13	1, 12	nfxfr 1645	1

Syntax hints:  -.wn 3  /\wa 369  A.wal 1393  wtru 1396  F/wnf 1616  e.wcel 1818  E*wmo 2283  F/_wnfc 2605  E*wrmo 2810

This theorem is referenced by:  2rmorex  3304  2reurex  32186

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-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-eu 2286  df-mo 2287  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rmo 2815