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Theorem sb8iota 5103
 Description: Variable substitution in description binder. Compare sb8eu 2013. (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 1509 . . . . . 6
21sb8 1829 . . . . 5
3 sbbi 1933 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 1920 . . . . . . . 8
6 equsb3 1925 . . . . . . . . 9
7 nfv 1509 . . . . . . . . 9
86, 7nfxfr 1451 . . . . . . . 8
95, 8nfbi 1569 . . . . . . 7
103, 9nfxfr 1451 . . . . . 6
11 nfv 1509 . . . . . 6
12 sbequ 1813 . . . . . 6
1310, 11, 12cbval 1728 . . . . 5
14 equsb3 1925 . . . . . . 7
1514sblbis 1934 . . . . . 6
1615albii 1447 . . . . 5
172, 13, 163bitri 205 . . . 4
1817abbii 2256 . . 3
1918unieqi 3754 . 2
20 dfiota2 5097 . 2
21 dfiota2 5097 . 2
2219, 20, 213eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1330   wceq 1332  wnf 1437  wsb 1736  cab 2126  cuni 3744  cio 5094 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 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-rex 2423  df-sn 3538  df-uni 3745  df-iota 5096 This theorem is referenced by: (None)
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