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Theorem rmyfval 26970
 Description: Value of the Y sequence. Not used after rmxyval 26980 is proved. (Contributed by Stefan O'Rear, 21-Sep-2014.)
Assertion
Ref Expression
rmyfval Yrm
Distinct variable groups:   ,   ,

Proof of Theorem rmyfval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq1 6090 . . . . . . . . . . 11
21oveq1d 6098 . . . . . . . . . 10
32fveq2d 5734 . . . . . . . . 9
43oveq1d 6098 . . . . . . . 8
54oveq2d 6099 . . . . . . 7
65mpteq2dv 4298 . . . . . 6
76cnveqd 5050 . . . . 5
87adantr 453 . . . 4
9 id 21 . . . . . 6
109, 3oveq12d 6101 . . . . 5
11 id 21 . . . . 5
1210, 11oveqan12d 6102 . . . 4
138, 12fveq12d 5736 . . 3
1413fveq2d 5734 . 2
15 df-rmy 26968 . 2 Yrm
16 fvex 5744 . 2
1714, 15, 16ovmpt2a 6206 1 Yrm
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   cmpt 4268   cxp 4878  ccnv 4879  cfv 5456  (class class class)co 6083  c1st 6349  c2nd 6350  c1 8993   caddc 8995   cmul 8997   cmin 9293  c2 10051  cn0 10223  cz 10284  cuz 10490  cexp 11384  csqr 12040   Yrm crmy 26966 This theorem is referenced by:  rmxyval  26980 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-sep 4332  ax-nul 4340  ax-pr 4405 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-mo 2288  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-opab 4269  df-mpt 4270  df-id 4500  df-xp 4886  df-rel 4887  df-cnv 4888  df-co 4889  df-dm 4890  df-iota 5420  df-fun 5458  df-fv 5464  df-ov 6086  df-oprab 6087  df-mpt2 6088  df-rmy 26968
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