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Theorem seqomeq12 7182
 Description: Equality theorem for seq𝜔. (Contributed by Stefan O'Rear, 1-Nov-2014.)
Assertion
Ref Expression
seqomeq12 seq𝜔 seq𝜔

Proof of Theorem seqomeq12
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq 6311 . . . . . 6
21opeq2d 4194 . . . . 5
32mpt2eq3dv 6371 . . . 4
4 fveq2 5881 . . . . 5
54opeq2d 4194 . . . 4
6 rdgeq12 7142 . . . 4
73, 5, 6syl2an 479 . . 3
87imaeq1d 5186 . 2
9 df-seqom 7176 . 2 seq𝜔
10 df-seqom 7176 . 2 seq𝜔
118, 9, 103eqtr4g 2488 1 seq𝜔 seq𝜔
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 370   wceq 1437  cvv 3080  c0 3761  cop 4004   cid 4763  cima 4856   csuc 5444  cfv 5601  (class class class)co 6305   cmpt2 6307  com 6706  crdg 7138  seq𝜔cseqom 7175 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2057  ax-ext 2401 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2568  df-ral 2776  df-rex 2777  df-rab 2780  df-v 3082  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3912  df-sn 3999  df-pr 4001  df-op 4005  df-uni 4220  df-br 4424  df-opab 4483  df-mpt 4484  df-xp 4859  df-cnv 4861  df-dm 4863  df-rn 4864  df-res 4865  df-ima 4866  df-pred 5399  df-iota 5565  df-fv 5609  df-ov 6308  df-oprab 6309  df-mpt2 6310  df-wrecs 7039  df-recs 7101  df-rdg 7139  df-seqom 7176 This theorem is referenced by:  cantnffval  8176  cantnfval  8181  cantnfres  8190  cnfcomlem  8212  cnfcom2  8215  fin23lem33  8782
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