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Definition df-altxp 31743
Description: Define Cartesian products of alternative ordered pairs. (Contributed by Scott Fenton, 23-Mar-2012.)
Assertion
Ref Expression
df-altxp (𝐴 ×× 𝐵) = {𝑧 ∣ ∃𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦⟫}
Distinct variable groups:   𝑥,𝐴,𝑦,𝑧   𝑥,𝐵,𝑦,𝑧

Detailed syntax breakdown of Definition df-altxp
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2caltxp 31741 . 2 class (𝐴 ×× 𝐵)
4 vz . . . . . . 7 setvar 𝑧
54cv 1479 . . . . . 6 class 𝑧
6 vx . . . . . . . 8 setvar 𝑥
76cv 1479 . . . . . . 7 class 𝑥
8 vy . . . . . . . 8 setvar 𝑦
98cv 1479 . . . . . . 7 class 𝑦
107, 9caltop 31740 . . . . . 6 class 𝑥, 𝑦
115, 10wceq 1480 . . . . 5 wff 𝑧 = ⟪𝑥, 𝑦
1211, 8, 2wrex 2908 . . . 4 wff 𝑦𝐵 𝑧 = ⟪𝑥, 𝑦
1312, 6, 1wrex 2908 . . 3 wff 𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦
1413, 4cab 2607 . 2 class {𝑧 ∣ ∃𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦⟫}
153, 14wceq 1480 1 wff (𝐴 ×× 𝐵) = {𝑧 ∣ ∃𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦⟫}
Colors of variables: wff setvar class
This definition is referenced by:  altxpeq1  31757  altxpeq2  31758  elaltxp  31759
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