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Theorem sb8iota 5563
 Description: Variable substitution in description binder. Compare sb8eu 2318. (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 1707 . . . . . 6
21sb8 2167 . . . . 5
3 sbbi 2142 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 2184 . . . . . . . 8
6 equsb3 2176 . . . . . . . . 9
7 nfv 1707 . . . . . . . . 9
86, 7nfxfr 1645 . . . . . . . 8
95, 8nfbi 1934 . . . . . . 7
103, 9nfxfr 1645 . . . . . 6
11 nfv 1707 . . . . . 6
12 sbequ 2117 . . . . . 6
1310, 11, 12cbval 2021 . . . . 5
14 equsb3 2176 . . . . . . 7
1514sblbis 2145 . . . . . 6
1615albii 1640 . . . . 5
172, 13, 163bitri 271 . . . 4
1817abbii 2591 . . 3
1918unieqi 4258 . 2
20 dfiota2 5557 . 2
21 dfiota2 5557 . 2
2219, 20, 213eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  <->wb 184  A.wal 1393  =wceq 1395  F/wnf 1616  [wsb 1739  {cab 2442  U.cuni 4249  iotacio 5554 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-sn 4030  df-uni 4250  df-iota 5556
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