Definition df-musyn 35612

Description: Define the syntax typecode function for the model universe. (Contributed by Mario Carneiro, 14-Jul-2016.)

Assertion

Ref	Expression
df-musyn	⊢ mUSyn = (𝑡 ∈ V ↦ (𝑣 ∈ (mUV‘𝑡) ↦ ⟨((mSyn‘𝑡)‘(1st ‘𝑣)), (2nd ‘𝑣)⟩))

Distinct variable group:   𝑣,𝑡

Detailed syntax breakdown of Definition df-musyn

Step	Hyp	Ref	Expression
1		cusyn 35601	. 2 class mUSyn
2		vt	. . 3 setvar 𝑡
3		cvv 3455	. . 3 class V
4		vv	. . . 4 setvar 𝑣
5	2	cv 1539	. . . . 5 class 𝑡
6		cmuv 35594	. . . . 5 class mUV
7	5, 6	cfv 6519	. . . 4 class (mUV‘𝑡)
8	4	cv 1539	. . . . . . 7 class 𝑣
9		c1st 7975	. . . . . . 7 class 1st
10	8, 9	cfv 6519	. . . . . 6 class (1st ‘𝑣)
11		cmsy 35577	. . . . . . 7 class mSyn
12	5, 11	cfv 6519	. . . . . 6 class (mSyn‘𝑡)
13	10, 12	cfv 6519	. . . . 5 class ((mSyn‘𝑡)‘(1st ‘𝑣))
14		c2nd 7976	. . . . . 6 class 2nd
15	8, 14	cfv 6519	. . . . 5 class (2nd ‘𝑣)
16	13, 15	cop 4603	. . . 4 class ⟨((mSyn‘𝑡)‘(1st ‘𝑣)), (2nd ‘𝑣)⟩
17	4, 7, 16	cmpt 5196	. . 3 class (𝑣 ∈ (mUV‘𝑡) ↦ ⟨((mSyn‘𝑡)‘(1st ‘𝑣)), (2nd ‘𝑣)⟩)
18	2, 3, 17	cmpt 5196	. 2 class (𝑡 ∈ V ↦ (𝑣 ∈ (mUV‘𝑡) ↦ ⟨((mSyn‘𝑡)‘(1st ‘𝑣)), (2nd ‘𝑣)⟩))
19	1, 18	wceq 1540	1 wff mUSyn = (𝑡 ∈ V ↦ (𝑣 ∈ (mUV‘𝑡) ↦ ⟨((mSyn‘𝑡)‘(1st ‘𝑣)), (2nd ‘𝑣)⟩))

This definition is referenced by: (None)