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Theorem nfiso 5389
 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 4854 . 2
2 nfiso.1 . . . 4
3 nfiso.4 . . . 4
4 nfiso.5 . . . 4
52, 3, 4nff1o 5067 . . 3
6 nfcv 2175 . . . . . . 7
7 nfiso.2 . . . . . . 7
8 nfcv 2175 . . . . . . 7
96, 7, 8nfbr 3799 . . . . . 6
102, 6nffv 5128 . . . . . . 7
11 nfiso.3 . . . . . . 7
122, 8nffv 5128 . . . . . . 7
1310, 11, 12nfbr 3799 . . . . . 6
149, 13nfbi 1478 . . . . 5
153, 14nfralxy 2354 . . . 4
163, 15nfralxy 2354 . . 3
175, 16nfan 1454 . 2
181, 17nfxfr 1360 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wnf 1346  wnfc 2162  wral 2300   class class class wbr 3755  wf1o 4844  cfv 4845   wiso 4846 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-uni 3572  df-br 3756  df-opab 3810  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-rn 4299  df-iota 4810  df-fun 4847  df-fn 4848  df-f 4849  df-f1 4850  df-fo 4851  df-f1o 4852  df-fv 4853  df-isom 4854 This theorem is referenced by: (None)
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