Definition df-mst 33543

Description: Define the function mapping syntax expressions to syntax trees. (Contributed by Mario Carneiro, 14-Jul-2016.)

Assertion

Ref	Expression
df-mst	⊢ mST = (𝑡 ∈ V ↦ ((∅(mTree‘𝑡)∅) ↾ ((mEx‘𝑡) ↾ (mVT‘𝑡))))

Detailed syntax breakdown of Definition df-mst

Step	Hyp	Ref	Expression
1		cmst 33533	. 2 class mST
2		vt	. . 3 setvar 𝑡
3		cvv 3430	. . 3 class V
4		c0 4261	. . . . 5 class ∅
5	2	cv 1540	. . . . . 6 class 𝑡
6		cmtree 33532	. . . . . 6 class mTree
7	5, 6	cfv 6430	. . . . 5 class (mTree‘𝑡)
8	4, 4, 7	co 7268	. . . 4 class (∅(mTree‘𝑡)∅)
9		cmex 33408	. . . . . 6 class mEx
10	5, 9	cfv 6430	. . . . 5 class (mEx‘𝑡)
11		cmvt 33404	. . . . . 6 class mVT
12	5, 11	cfv 6430	. . . . 5 class (mVT‘𝑡)
13	10, 12	cres 5590	. . . 4 class ((mEx‘𝑡) ↾ (mVT‘𝑡))
14	8, 13	cres 5590	. . 3 class ((∅(mTree‘𝑡)∅) ↾ ((mEx‘𝑡) ↾ (mVT‘𝑡)))
15	2, 3, 14	cmpt 5161	. 2 class (𝑡 ∈ V ↦ ((∅(mTree‘𝑡)∅) ↾ ((mEx‘𝑡) ↾ (mVT‘𝑡))))
16	1, 15	wceq 1541	1 wff mST = (𝑡 ∈ V ↦ ((∅(mTree‘𝑡)∅) ↾ ((mEx‘𝑡) ↾ (mVT‘𝑡))))

This definition is referenced by: (None)