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Theorem sb8iota 5570
 Description: Variable substitution in description binder. Compare sb8eu 2300. (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 1752 . . . . . 6
21sb8 2219 . . . . 5
3 sbbi 2196 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 2236 . . . . . . . 8
6 equsb3 2228 . . . . . . . . 9
7 nfv 1752 . . . . . . . . 9
86, 7nfxfr 1693 . . . . . . . 8
95, 8nfbi 1991 . . . . . . 7
103, 9nfxfr 1693 . . . . . 6
11 nfv 1752 . . . . . 6
12 sbequ 2171 . . . . . 6
1310, 11, 12cbval 2076 . . . . 5
14 equsb3 2228 . . . . . . 7
1514sblbis 2199 . . . . . 6
1615albii 1688 . . . . 5
172, 13, 163bitri 275 . . . 4
1817abbii 2557 . . 3
1918unieqi 4226 . 2
20 dfiota2 5564 . 2
21 dfiota2 5564 . 2
2219, 20, 213eqtr4i 2462 1
 Colors of variables: wff setvar class Syntax hints:   wb 188  wal 1436   wceq 1438  wnf 1664  wsb 1787  cab 2408  cuni 4217  cio 5561 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-rex 2782  df-sn 3998  df-uni 4218  df-iota 5563 This theorem is referenced by: (None)
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