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Theorem seqomeq12 6711
 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 6087 . . . . . . 7
21opeq2d 3991 . . . . . 6
323ad2ant1 978 . . . . 5
43mpt2eq3dva 6138 . . . 4
5 fveq2 5728 . . . . 5
65opeq2d 3991 . . . 4
7 rdgeq12 6671 . . . 4
84, 6, 7syl2an 464 . . 3
98imaeq1d 5202 . 2
10 df-seqom 6705 . 2 seq𝜔
11 df-seqom 6705 . 2 seq𝜔
129, 10, 113eqtr4g 2493 1 seq𝜔 seq𝜔
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359   wceq 1652   wcel 1725  cvv 2956  c0 3628  cop 3817   cid 4493   csuc 4583  com 4845  cima 4881  cfv 5454  (class class class)co 6081   cmpt2 6083  crdg 6667  seq𝜔cseqom 6704 This theorem is referenced by:  cantnffval  7618  cantnfval  7623  cantnfres  7633  cnfcomlem  7656  cnfcom2  7659  fin23lem33  8225 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 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-br 4213  df-opab 4267  df-mpt 4268  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891  df-iota 5418  df-fv 5462  df-ov 6084  df-oprab 6085  df-mpt2 6086  df-recs 6633  df-rdg 6668  df-seqom 6705
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