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Theorem iotassuni 5426
 Description: The class is a subset of the union of all elements satisfying . (Contributed by Mario Carneiro, 24-Dec-2016.)
Assertion
Ref Expression
iotassuni

Proof of Theorem iotassuni
StepHypRef Expression
1 iotauni 5422 . . 3
2 eqimss 3392 . . 3
31, 2syl 16 . 2
4 iotanul 5425 . . 3
5 0ss 3648 . . 3
64, 5syl6eqss 3390 . 2
73, 6pm2.61i 158 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1652  weu 2280  cab 2421   wss 3312  c0 3620  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-eu 2284  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-sn 3812  df-pr 3813  df-uni 4008  df-iota 5410
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