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Theorem sb8iota 5417
 Description: Variable substitution in description binder. Compare sb8eu 2298. (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 1629 . . . . . 6
21sb8 2167 . . . . 5
3 sbbi 2145 . . . . . . 7
4 sb8iota.1 . . . . . . . . 9
54nfsb 2184 . . . . . . . 8
6 equsb3 2177 . . . . . . . . 9
7 nfv 1629 . . . . . . . . 9
86, 7nfxfr 1579 . . . . . . . 8
95, 8nfbi 1856 . . . . . . 7
103, 9nfxfr 1579 . . . . . 6
11 nfv 1629 . . . . . 6
12 sbequ 2138 . . . . . 6
1310, 11, 12cbval 1982 . . . . 5
14 equsb3 2177 . . . . . . 7
1514sblbis 2146 . . . . . 6
1615albii 1575 . . . . 5
172, 13, 163bitri 263 . . . 4
1817abbii 2547 . . 3
1918unieqi 4017 . 2
20 dfiota2 5411 . 2
21 dfiota2 5411 . 2
2219, 20, 213eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wb 177  wal 1549  wnf 1553   wceq 1652  wsb 1658  cab 2421  cuni 4007  cio 5408 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rex 2703  df-sn 3812  df-uni 4008  df-iota 5410
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