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Theorem sb8iota 4874
 Description: Variable substitution in description binder. Compare sb8eu 1913. (Contributed by NM, 18-Mar-2013.)
Hypothesis
Ref Expression
sb8iota.1
Assertion
Ref Expression
sb8iota

Proof of Theorem sb8iota
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 nfv 1421 . . . . . 6
21sb8 1736 . . . . 5
3 sbbi 1833 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 1822 . . . . . . . 8
6 equsb3 1825 . . . . . . . . 9
7 nfv 1421 . . . . . . . . 9
86, 7nfxfr 1363 . . . . . . . 8
95, 8nfbi 1481 . . . . . . 7
103, 9nfxfr 1363 . . . . . 6
11 nfv 1421 . . . . . 6
12 sbequ 1721 . . . . . 6
1310, 11, 12cbval 1637 . . . . 5
14 equsb3 1825 . . . . . . 7
1514sblbis 1834 . . . . . 6
1615albii 1359 . . . . 5
172, 13, 163bitri 195 . . . 4
1817abbii 2153 . . 3
1918unieqi 3590 . 2
20 dfiota2 4868 . 2
21 dfiota2 4868 . 2
2219, 20, 213eqtr4i 2070 1
 Colors of variables: wff set class Syntax hints:   wb 98  wal 1241   wceq 1243  wnf 1349  wsb 1645  cab 2026  cuni 3580  cio 4865 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rex 2312  df-sn 3381  df-uni 3581  df-iota 4867 This theorem is referenced by: (None)
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