Mathbox for Stefan O'Rear < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  rmxfval Structured version   Unicode version

Theorem rmxfval 26968
 Description: Value of the X sequence. Not used after rmxyval 26979 is proved. (Contributed by Stefan O'Rear, 21-Sep-2014.)
Assertion
Ref Expression
rmxfval Xrm
Distinct variable groups:   ,   ,

Proof of Theorem rmxfval
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 oveq1 6089 . . . . . . . . . . 11
21oveq1d 6097 . . . . . . . . . 10
32fveq2d 5733 . . . . . . . . 9
43oveq1d 6097 . . . . . . . 8
54oveq2d 6098 . . . . . . 7
65mpteq2dv 4297 . . . . . 6
76cnveqd 5049 . . . . 5
87adantr 453 . . . 4
9 id 21 . . . . . 6
109, 3oveq12d 6100 . . . . 5
11 id 21 . . . . 5
1210, 11oveqan12d 6101 . . . 4
138, 12fveq12d 5735 . . 3
1413fveq2d 5733 . 2
15 df-rmx 26966 . 2 Xrm
16 fvex 5743 . 2
1714, 15, 16ovmpt2a 6205 1 Xrm
 Colors of variables: wff set class Syntax hints:   wi 4   wa 360   wceq 1653   wcel 1726   cmpt 4267   cxp 4877  ccnv 4878  cfv 5455  (class class class)co 6082  c1st 6348  c2nd 6349  c1 8992   caddc 8994   cmul 8996   cmin 9292  c2 10050  cn0 10222  cz 10283  cuz 10489  cexp 11383  csqr 12039   Xrm crmx 26964 This theorem is referenced by:  rmxyval  26979 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 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 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 2286  df-mo 2287  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-sbc 3163  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-uni 4017  df-br 4214  df-opab 4268  df-mpt 4269  df-id 4499  df-xp 4885  df-rel 4886  df-cnv 4887  df-co 4888  df-dm 4889  df-iota 5419  df-fun 5457  df-fv 5463  df-ov 6085  df-oprab 6086  df-mpt2 6087  df-rmx 26966
 Copyright terms: Public domain W3C validator