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Theorem iotain 36838
 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 2323 . 2
2 vex 3034 . . . . 5
32intsn 4262 . . . 4
4 nfa1 1999 . . . . . . 7
5 sp 1957 . . . . . . 7
64, 5abbid 2588 . . . . . 6
7 df-sn 3960 . . . . . 6
86, 7syl6eqr 2523 . . . . 5
98inteqd 4231 . . . 4
10 iotaval 5564 . . . 4
113, 9, 103eqtr4a 2531 . . 3
1211exlimiv 1784 . 2
131, 12sylbi 200 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 189  wal 1450   wceq 1452  wex 1671  weu 2319  cab 2457  csn 3959  cint 4226  cio 5551 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-v 3033  df-sbc 3256  df-un 3395  df-in 3397  df-sn 3960  df-pr 3962  df-uni 4191  df-int 4227  df-iota 5553 This theorem is referenced by: (None)
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