Definition df-txp 36365

Description: Define the tail cross of two classes. Membership in this class is defined by txpss3v 36389 and brtxp 36391. (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 36341	. 2 class (𝐴 ⊗ 𝐵)
4		c1st 7993	. . . . . 6 class 1st
5		cvv 3458	. . . . . . 7 class V
6	5, 5	cxp 5664	. . . . . 6 class (V × V)
7	4, 6	cres 5668	. . . . 5 class (1st ↾ (V × V))
8	7	ccnv 5665	. . . 4 class ◡(1st ↾ (V × V))
9	8, 1	ccom 5670	. . 3 class (◡(1st ↾ (V × V)) ∘ 𝐴)
10		c2nd 7994	. . . . . 6 class 2nd
11	10, 6	cres 5668	. . . . 5 class (2nd ↾ (V × V))
12	11	ccnv 5665	. . . 4 class ◡(2nd ↾ (V × V))
13	12, 2	ccom 5670	. . 3 class (◡(2nd ↾ (V × V)) ∘ 𝐵)
14	9, 13	cin 3907	. 2 class ((◡(1st ↾ (V × V)) ∘ 𝐴) ∩ (◡(2nd ↾ (V × V)) ∘ 𝐵))
15	3, 14	wceq 1570	1 wff (𝐴 ⊗ 𝐵) = ((◡(1st ↾ (V × V)) ∘ 𝐴) ∩ (◡(2nd ↾ (V × V)) ∘ 𝐵))

This definition is used by:  txpss3v  36389  brtxp  36391  dfpprod2  36393