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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.
StepHypRef Expression
1 df-isom 5602 . 2
2 nfiso.1 . . . 4
3 nfiso.4 . . . 4
4 nfiso.5 . . . 4
52, 3, 4nff1o 5819 . . 3
6 nfcv 2619 . . . . . . 7
7 nfiso.2 . . . . . . 7
8 nfcv 2619 . . . . . . 7
96, 7, 8nfbr 4496 . . . . . 6
102, 6nffv 5878 . . . . . . 7
11 nfiso.3 . . . . . . 7
122, 8nffv 5878 . . . . . . 7
1310, 11, 12nfbr 4496 . . . . . 6
149, 13nfbi 1934 . . . . 5
153, 14nfral 2843 . . . 4
163, 15nfral 2843 . . 3
175, 16nfan 1928 . 2
181, 17nfxfr 1645 1
 Colors of variables: wff setvar class 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  Isom`wiso 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
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