Users' Mathboxes Mathbox for Mario Carneiro < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-mvrs Structured version   Visualization version   GIF version

Definition df-mvrs 30640
Description: Define the set of variables in an expression. (Contributed by Mario Carneiro, 14-Jul-2016.)
Assertion
Ref Expression
df-mvrs mVars = (𝑡 ∈ V ↦ (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡))))
Distinct variable group:   𝑡,𝑒

Detailed syntax breakdown of Definition df-mvrs
StepHypRef Expression
1 cmvrs 30620 . 2 class mVars
2 vt . . 3 setvar 𝑡
3 cvv 3173 . . 3 class V
4 ve . . . 4 setvar 𝑒
52cv 1474 . . . . 5 class 𝑡
6 cmex 30618 . . . . 5 class mEx
75, 6cfv 5804 . . . 4 class (mEx‘𝑡)
84cv 1474 . . . . . . 7 class 𝑒
9 c2nd 7058 . . . . . . 7 class 2nd
108, 9cfv 5804 . . . . . 6 class (2nd𝑒)
1110crn 5039 . . . . 5 class ran (2nd𝑒)
12 cmvar 30612 . . . . . 6 class mVR
135, 12cfv 5804 . . . . 5 class (mVR‘𝑡)
1411, 13cin 3539 . . . 4 class (ran (2nd𝑒) ∩ (mVR‘𝑡))
154, 7, 14cmpt 4643 . . 3 class (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡)))
162, 3, 15cmpt 4643 . 2 class (𝑡 ∈ V ↦ (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡))))
171, 16wceq 1475 1 wff mVars = (𝑡 ∈ V ↦ (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡))))
Colors of variables: wff setvar class
This definition is referenced by:  mvrsval  30656
  Copyright terms: Public domain W3C validator