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Theorem nfiso 6047
 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 5466 . 2
2 nfiso.1 . . . 4
3 nfiso.4 . . . 4
4 nfiso.5 . . . 4
52, 3, 4nff1o 5675 . . 3
6 nfcv 2574 . . . . . . 7
7 nfiso.2 . . . . . . 7
8 nfcv 2574 . . . . . . 7
96, 7, 8nfbr 4259 . . . . . 6
102, 6nffv 5738 . . . . . . 7
11 nfiso.3 . . . . . . 7
122, 8nffv 5738 . . . . . . 7
1310, 11, 12nfbr 4259 . . . . . 6
149, 13nfbi 1857 . . . . 5
153, 14nfral 2761 . . . 4
163, 15nfral 2761 . . 3
175, 16nfan 1847 . 2
181, 17nfxfr 1580 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360  wnf 1554  wnfc 2561  wral 2707   class class class wbr 4215  wf1o 5456  cfv 5457   wiso 5458 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4216  df-opab 4270  df-rel 4888  df-cnv 4889  df-co 4890  df-dm 4891  df-rn 4892  df-iota 5421  df-fun 5459  df-fn 5460  df-f 5461  df-f1 5462  df-fo 5463  df-f1o 5464  df-fv 5465  df-isom 5466
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