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Theorem iotassuni 5251
 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 5247 . . 3
2 eqimss 3243 . . 3
31, 2syl 15 . 2
4 0ss 3496 . . 3
5 iotanul 5250 . . . 4
65sseq1d 3218 . . 3
74, 6mpbiri 224 . 2
83, 7pm2.61i 156 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1632  weu 2156  cab 2282   wss 3165  c0 3468  cuni 3843  cio 5233 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235
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