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Theorem seqomeq12 7138
 Description: Equality theorem for seqom. (Contributed by Stefan O'Rear, 1-Nov-2014.)
Assertion
Ref Expression
seqomeq12

Proof of Theorem seqomeq12
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq 6302 . . . . . 6
21opeq2d 4224 . . . . 5
32mpt2eq3dv 6363 . . . 4
4 fveq2 5871 . . . . 5
54opeq2d 4224 . . . 4
6 rdgeq12 7098 . . . 4
73, 5, 6syl2an 477 . . 3
87imaeq1d 5341 . 2
9 df-seqom 7132 . 2
10 df-seqom 7132 . 2
118, 9, 103eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395   cvv 3109   c0 3784  <.cop 4035   cid 4795  succsuc 4885  "cima 5007  cfv 5593  (class class class)co 6296  e.cmpt2 6298   com 6700  reccrdg 7094  seqom`cseqom 7131 This theorem is referenced by:  cantnffval  8101  cantnfval  8108  cantnfres  8117  cantnfvalOLD  8138  cnfcomlem  8164  cnfcom2  8167  cnfcomlemOLD  8172  cnfcom2OLD  8175  fin23lem33  8746 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-mpt 4512  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fv 5601  df-ov 6299  df-oprab 6300  df-mpt2 6301  df-recs 7061  df-rdg 7095  df-seqom 7132
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