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Definition df-txp 31945
Description: Define the tail cross of two classes. Membership in this class is defined by txpss3v 31969 and brtxp 31971. (Contributed by Scott Fenton, 31-Mar-2012.)
Assertion
Ref Expression
df-txp (𝐴𝐵) = (((1st ↾ (V × V)) ∘ 𝐴) ∩ ((2nd ↾ (V × V)) ∘ 𝐵))

Detailed syntax breakdown of Definition df-txp
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2ctxp 31921 . 2 class (𝐴𝐵)
4 c1st 7163 . . . . . 6 class 1st
5 cvv 3198 . . . . . . 7 class V
65, 5cxp 5110 . . . . . 6 class (V × V)
74, 6cres 5114 . . . . 5 class (1st ↾ (V × V))
87ccnv 5111 . . . 4 class (1st ↾ (V × V))
98, 1ccom 5116 . . 3 class ((1st ↾ (V × V)) ∘ 𝐴)
10 c2nd 7164 . . . . . 6 class 2nd
1110, 6cres 5114 . . . . 5 class (2nd ↾ (V × V))
1211ccnv 5111 . . . 4 class (2nd ↾ (V × V))
1312, 2ccom 5116 . . 3 class ((2nd ↾ (V × V)) ∘ 𝐵)
149, 13cin 3571 . 2 class (((1st ↾ (V × V)) ∘ 𝐴) ∩ ((2nd ↾ (V × V)) ∘ 𝐵))
153, 14wceq 1482 1 wff (𝐴𝐵) = (((1st ↾ (V × V)) ∘ 𝐴) ∩ ((2nd ↾ (V × V)) ∘ 𝐵))
Colors of variables: wff setvar class
This definition is referenced by:  txpss3v  31969  brtxp  31971  dfpprod2  31973
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