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Definition df-mvrs 31724
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 31704 . 2 class mVars
2 vt . . 3 setvar 𝑡
3 cvv 3351 . . 3 class V
4 ve . . . 4 setvar 𝑒
52cv 1630 . . . . 5 class 𝑡
6 cmex 31702 . . . . 5 class mEx
75, 6cfv 6031 . . . 4 class (mEx‘𝑡)
84cv 1630 . . . . . . 7 class 𝑒
9 c2nd 7314 . . . . . . 7 class 2nd
108, 9cfv 6031 . . . . . 6 class (2nd𝑒)
1110crn 5250 . . . . 5 class ran (2nd𝑒)
12 cmvar 31696 . . . . . 6 class mVR
135, 12cfv 6031 . . . . 5 class (mVR‘𝑡)
1411, 13cin 3722 . . . 4 class (ran (2nd𝑒) ∩ (mVR‘𝑡))
154, 7, 14cmpt 4863 . . 3 class (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡)))
162, 3, 15cmpt 4863 . 2 class (𝑡 ∈ V ↦ (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡))))
171, 16wceq 1631 1 wff mVars = (𝑡 ∈ V ↦ (𝑒 ∈ (mEx‘𝑡) ↦ (ran (2nd𝑒) ∩ (mVR‘𝑡))))
Colors of variables: wff setvar class
This definition is referenced by:  mvrsval  31740
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