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Theorem itunifval 8327
 Description: Function value of iterated unions. EDITORIAL: The iterated unions and order types of ordered sets are split out here because they could concievably be independently useful. (Contributed by Stefan O'Rear, 11-Feb-2015.)
Hypothesis
Ref Expression
ituni.u
Assertion
Ref Expression
itunifval
Distinct variable group:   ,,
Allowed substitution hints:   (,)   (,)

Proof of Theorem itunifval
StepHypRef Expression
1 elex 2970 . 2
2 rdgeq2 6699 . . . 4
32reseq1d 5174 . . 3
4 ituni.u . . 3
5 rdgfun 6703 . . . 4
6 omex 7627 . . . 4
7 resfunexg 5986 . . . 4
85, 6, 7mp2an 655 . . 3
93, 4, 8fvmpt 5835 . 2
101, 9syl 16 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1727  cvv 2962  cuni 4039   cmpt 4291  com 4874   cres 4909   wfun 5477  cfv 5483  crdg 6696 This theorem is referenced by:  itunifn  8328  ituni0  8329  itunisuc  8330 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-13 1729  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-rep 4345  ax-sep 4355  ax-nul 4363  ax-pow 4406  ax-pr 4432  ax-un 4730  ax-inf2 7625 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3or 938  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-reu 2718  df-rab 2720  df-v 2964  df-sbc 3168  df-csb 3268  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-pss 3322  df-nul 3614  df-if 3764  df-pw 3825  df-sn 3844  df-pr 3845  df-tp 3846  df-op 3847  df-uni 4040  df-iun 4119  df-br 4238  df-opab 4292  df-mpt 4293  df-tr 4328  df-eprel 4523  df-id 4527  df-po 4532  df-so 4533  df-fr 4570  df-we 4572  df-ord 4613  df-on 4614  df-lim 4615  df-suc 4616  df-om 4875  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-rn 4918  df-res 4919  df-ima 4920  df-iota 5447  df-fun 5485  df-fn 5486  df-f 5487  df-f1 5488  df-fo 5489  df-f1o 5490  df-fv 5491  df-recs 6662  df-rdg 6697
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