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Theorem sb8iota 4346
 Description: Variable substitution in description binder. Compare sb8eu 2222. (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 1619 . . . . . 6
21sb8 2092 . . . . 5
3 sbbi 2071 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 2109 . . . . . . . 8
6 equsb3 2102 . . . . . . . . 9
7 nfv 1619 . . . . . . . . 9
86, 7nfxfr 1570 . . . . . . . 8
95, 8nfbi 1834 . . . . . . 7
103, 9nfxfr 1570 . . . . . 6
11 nfv 1619 . . . . . 6
12 sbequ 2060 . . . . . 6
1310, 11, 12cbval 1984 . . . . 5
14 equsb3 2102 . . . . . . 7
1514sblbis 2072 . . . . . 6
1615albii 1566 . . . . 5
172, 13, 163bitri 262 . . . 4
1817abbii 2465 . . 3
1918unieqi 3901 . 2
20 dfiota2 4340 . 2
21 dfiota2 4340 . 2
2219, 20, 213eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wb 176  wal 1540  wnf 1544   wceq 1642  wsb 1648  cab 2339  cuni 3891  cio 4337 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-rex 2620  df-sn 3741  df-uni 3892  df-iota 4339 This theorem is referenced by: (None)
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