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Theorem isrgra 24749
 Description: The property of being a k-regular graph. (Contributed by Alexander van der Vekens, 7-Jul-2018.)
Assertion
Ref Expression
isrgra RegGrph VDeg
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem isrgra
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-br 4454 . 2 RegGrph RegGrph
2 df-rgra 24747 . . . 4 RegGrph VDeg
32eleq2i 2545 . . 3 RegGrph VDeg
4 eleq1 2539 . . . . . 6
543ad2ant3 1019 . . . . 5
6 simp1 996 . . . . . 6
7 oveq12 6304 . . . . . . . . 9 VDeg VDeg
87fveq1d 5874 . . . . . . . 8 VDeg VDeg
983adant3 1016 . . . . . . 7 VDeg VDeg
10 simp3 998 . . . . . . 7
119, 10eqeq12d 2489 . . . . . 6 VDeg VDeg
126, 11raleqbidv 3077 . . . . 5 VDeg VDeg
135, 12anbi12d 710 . . . 4 VDeg VDeg
1413eloprabga 6384 . . 3 VDeg VDeg
153, 14syl5bb 257 . 2 RegGrph VDeg
161, 15syl5bb 257 1 RegGrph VDeg
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   w3a 973   wceq 1379   wcel 1767  wral 2817  cop 4039   class class class wbr 4453  cfv 5594  (class class class)co 6295  coprab 6296  cn0 10807   VDeg cvdg 24716   RegGrph crgra 24745 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-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pr 4692 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-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-iota 5557  df-fv 5602  df-ov 6298  df-oprab 6299  df-rgra 24747 This theorem is referenced by:  isrusgra  24750  rgraprop  24751  rusgrargra  24753  isrusgusrg  24755  isrgrac  24757  0egra0rgra  24759  0vgrargra  24760
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