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Theorem rgraprop 24604
 Description: The properties of a k-regular graph. (Contributed by Alexander van der Vekens, 8-Jul-2018.)
Assertion
Ref Expression
rgraprop RegGrph VDeg
Distinct variable groups:   ,   ,   ,

Proof of Theorem rgraprop
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rgra 24600 . . . 4 RegGrph VDeg
21breqi 4453 . . 3 RegGrph VDeg
3 oprabv 6327 . . 3 VDeg
42, 3sylbi 195 . 2 RegGrph
5 isrgra 24602 . . 3 RegGrph VDeg
65biimpd 207 . 2 RegGrph VDeg
74, 6mpcom 36 1 RegGrph VDeg
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 369   w3a 973   wceq 1379   wcel 1767  wral 2814  cvv 3113  cop 4033   class class class wbr 4447  cfv 5586  (class class class)co 6282  coprab 6283  cn0 10791   VDeg cvdg 24569   RegGrph crgra 24598 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 4568  ax-nul 4576  ax-pr 4686 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-ral 2819  df-rex 2820  df-rab 2823  df-v 3115  df-sbc 3332  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-uni 4246  df-br 4448  df-opab 4506  df-xp 5005  df-rel 5006  df-iota 5549  df-fv 5594  df-ov 6285  df-oprab 6286  df-rgra 24600 This theorem is referenced by:  0eusgraiff0rgra  24615
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