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Theorem nfiso 5707
 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 5132 . 2
2 nfiso.1 . . . 4
3 nfiso.4 . . . 4
4 nfiso.5 . . . 4
52, 3, 4nff1o 5365 . . 3
6 nfcv 2281 . . . . . . 7
7 nfiso.2 . . . . . . 7
8 nfcv 2281 . . . . . . 7
96, 7, 8nfbr 3974 . . . . . 6
102, 6nffv 5431 . . . . . . 7
11 nfiso.3 . . . . . . 7
122, 8nffv 5431 . . . . . . 7
1310, 11, 12nfbr 3974 . . . . . 6
149, 13nfbi 1568 . . . . 5
153, 14nfralxy 2471 . . . 4
163, 15nfralxy 2471 . . 3
175, 16nfan 1544 . 2
181, 17nfxfr 1450 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wnf 1436  wnfc 2268  wral 2416   class class class wbr 3929  wf1o 5122  cfv 5123   wiso 5124 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-sn 3533  df-pr 3534  df-op 3536  df-uni 3737  df-br 3930  df-opab 3990  df-rel 4546  df-cnv 4547  df-co 4548  df-dm 4549  df-rn 4550  df-iota 5088  df-fun 5125  df-fn 5126  df-f 5127  df-f1 5128  df-fo 5129  df-f1o 5130  df-fv 5131  df-isom 5132 This theorem is referenced by: (None)
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