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Theorem seqeq2 12111
 Description: Equality theorem for the sequence builder operation. (Contributed by Mario Carneiro, 4-Sep-2013.)
Assertion
Ref Expression
seqeq2

Proof of Theorem seqeq2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq 6302 . . . . . 6
21opeq2d 4224 . . . . 5
32mpt2eq3dv 6363 . . . 4
4 rdgeq1 7096 . . . 4
53, 4syl 16 . . 3
65imaeq1d 5341 . 2
7 df-seq 12108 . 2
8 df-seq 12108 . 2
96, 7, 83eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395   cvv 3109  <.cop 4035  "cima 5007  cfv 5593  (class class class)co 6296  e.cmpt2 6298   com 6700  reccrdg 7094  1c1 9514   caddc 9516  seq`cseq 12107 This theorem is referenced by:  seqeq2d  12114  sadcom  14113  gxfval  25259  ressmulgnn  27671  cvmliftlem15  28743 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-seq 12108
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