Mathbox for Norm Megill < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  riotasvd Structured version   Unicode version

Theorem riotasvd 34160
 Description: Deduction version of riotasv 34163. (Contributed by NM, 4-Mar-2013.) (Revised by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
riotasvd.1
riotasvd.2
Assertion
Ref Expression
riotasvd
Distinct variable groups:   ,,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()   (,)   (,)

Proof of Theorem riotasvd
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 riotasvd.1 . . . . . . . . 9
21adantr 465 . . . . . . . 8
3 riotasvd.2 . . . . . . . . 9
43adantr 465 . . . . . . . 8
52, 4eqeltrrd 2556 . . . . . . 7
6 riotaclbgBAD 34158 . . . . . . . 8
76adantl 466 . . . . . . 7
85, 7mpbird 232 . . . . . 6
9 riotasbc 6272 . . . . . 6
108, 9syl 16 . . . . 5
11 eqeq1 2471 . . . . . . . . 9
1211imbi2d 316 . . . . . . . 8
1312ralbidv 2906 . . . . . . 7
14 nfra1 2848 . . . . . . . . . 10
15 nfcv 2629 . . . . . . . . . 10
1614, 15nfriota 6265 . . . . . . . . 9
1716nfeq2 2646 . . . . . . . 8
18 eqeq1 2471 . . . . . . . . 9
1918imbi2d 316 . . . . . . . 8
2017, 19ralbid 2901 . . . . . . 7
2113, 20sbcie2g 3370 . . . . . 6
225, 21syl 16 . . . . 5
2310, 22mpbid 210 . . . 4
24 rsp 2833 . . . 4
2523, 24syl 16 . . 3
2625impd 431 . 2
272eqeq1d 2469 . 2
2826, 27sylibrd 234 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379   wcel 1767  wral 2817  wreu 2819  wsbc 3336  crio 6255 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692  ax-un 6587  ax-riotaBAD 34157 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-nel 2665  df-ral 2822  df-rex 2823  df-reu 2824  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-pw 4018  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-iota 5557  df-fun 5596  df-fv 5602  df-riota 6256  df-undef 7014 This theorem is referenced by:  riotasv2d  34161  riotasv  34163  riotasv3d  34164  cdleme32a  35638
 Copyright terms: Public domain W3C validator