Theorem nfiso 6220

Description: Bound-variable hypothesis builder for an isomorphism. (Contributed by NM, 17-May-2004.) (Proof shortened by Andrew Salmon, 22-Oct-2011.)

Hypotheses

Ref	Expression
nfiso.1
nfiso.2
nfiso.3
nfiso.4
nfiso.5

Assertion

Ref	Expression
nfiso

Proof of Theorem nfiso

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

Step	Hyp	Ref	Expression
1		df-isom 5602	. 2
2		nfiso.1	. . . 4
3		nfiso.4	. . . 4
4		nfiso.5	. . . 4
5	2, 3, 4	nff1o 5819	. . 3
6		nfcv 2619	. . . . . . 7
7		nfiso.2	. . . . . . 7
8		nfcv 2619	. . . . . . 7
9	6, 7, 8	nfbr 4496	. . . . . 6
10	2, 6	nffv 5878	. . . . . . 7
11		nfiso.3	. . . . . . 7
12	2, 8	nffv 5878	. . . . . . 7
13	10, 11, 12	nfbr 4496	. . . . . 6
14	9, 13	nfbi 1934	. . . . 5
15	3, 14	nfral 2843	. . . 4
16	3, 15	nfral 2843	. . 3
17	5, 16	nfan 1928	. 2
18	1, 17	nfxfr 1645	1

Syntax hints:  <->wb 184  /\wa 369  F/wnf 1616  F/_wnfc 2605  A.wral 2807   class class class wbr 4452  -1-1-onto->wf1o 5592  `cfv 5593  Isomwiso 5594

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-uni 4250  df-br 4453  df-opab 4511  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-f 5597  df-f1 5598  df-fo 5599  df-f1o 5600  df-fv 5601  df-isom 5602