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Theorem iotain 27632
 Description: Equivalence between two different forms of . (Contributed by Andrew Salmon, 15-Jul-2011.)
Assertion
Ref Expression
iotain

Proof of Theorem iotain
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-eu 2291 . 2
2 vex 2965 . . . . 5
32intsn 4110 . . . 4
4 nfa1 1808 . . . . . . 7
5 sp 1765 . . . . . . 7
64, 5abbid 2555 . . . . . 6
7 df-sn 3844 . . . . . 6
86, 7syl6eqr 2492 . . . . 5
98inteqd 4079 . . . 4
10 iotaval 5458 . . . 4
113, 9, 103eqtr4a 2500 . . 3
1211exlimiv 1645 . 2
131, 12sylbi 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178  wal 1550  wex 1551   wceq 1653  weu 2287  cab 2428  csn 3838  cint 4074  cio 5445 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ral 2716  df-rex 2717  df-v 2964  df-sbc 3168  df-un 3311  df-in 3313  df-sn 3844  df-pr 3845  df-uni 4040  df-int 4075  df-iota 5447
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