Definition df-txp 31130

Description: Define the tail cross of two classes. Membership in this class is defined by txpss3v 31155 and brtxp 31157. (Contributed by Scott Fenton, 31-Mar-2012.)

Assertion

Ref	Expression
df-txp	⊢ (𝐴 ⊗ 𝐵) = ((◡(1st ↾ (V × V)) ∘ 𝐴) ∩ (◡(2nd ↾ (V × V)) ∘ 𝐵))

Detailed syntax breakdown of Definition df-txp

Step	Hyp	Ref	Expression
1		cA	. . 3 class 𝐴
2		cB	. . 3 class 𝐵
3	1, 2	ctxp 31106	. 2 class (𝐴 ⊗ 𝐵)
4		c1st 7057	. . . . . 6 class 1st
5		cvv 3173	. . . . . . 7 class V
6	5, 5	cxp 5036	. . . . . 6 class (V × V)
7	4, 6	cres 5040	. . . . 5 class (1st ↾ (V × V))
8	7	ccnv 5037	. . . 4 class ◡(1st ↾ (V × V))
9	8, 1	ccom 5042	. . 3 class (◡(1st ↾ (V × V)) ∘ 𝐴)
10		c2nd 7058	. . . . . 6 class 2nd
11	10, 6	cres 5040	. . . . 5 class (2nd ↾ (V × V))
12	11	ccnv 5037	. . . 4 class ◡(2nd ↾ (V × V))
13	12, 2	ccom 5042	. . 3 class (◡(2nd ↾ (V × V)) ∘ 𝐵)
14	9, 13	cin 3539	. 2 class ((◡(1st ↾ (V × V)) ∘ 𝐴) ∩ (◡(2nd ↾ (V × V)) ∘ 𝐵))
15	3, 14	wceq 1475	1 wff (𝐴 ⊗ 𝐵) = ((◡(1st ↾ (V × V)) ∘ 𝐴) ∩ (◡(2nd ↾ (V × V)) ∘ 𝐵))

This definition is referenced by:  txpss3v  31155  brtxp  31157  dfpprod2  31159