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Definition df-altxp 31236
 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 31234 . 2 class (𝐴 ×× 𝐵)
4 vz . . . . . . 7 setvar 𝑧
54cv 1474 . . . . . 6 class 𝑧
6 vx . . . . . . . 8 setvar 𝑥
76cv 1474 . . . . . . 7 class 𝑥
8 vy . . . . . . . 8 setvar 𝑦
98cv 1474 . . . . . . 7 class 𝑦
107, 9caltop 31233 . . . . . 6 class 𝑥, 𝑦
115, 10wceq 1475 . . . . 5 wff 𝑧 = ⟪𝑥, 𝑦
1211, 8, 2wrex 2897 . . . 4 wff 𝑦𝐵 𝑧 = ⟪𝑥, 𝑦
1312, 6, 1wrex 2897 . . 3 wff 𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦
1413, 4cab 2596 . 2 class {𝑧 ∣ ∃𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦⟫}
153, 14wceq 1475 1 wff (𝐴 ×× 𝐵) = {𝑧 ∣ ∃𝑥𝐴𝑦𝐵 𝑧 = ⟪𝑥, 𝑦⟫}
 Colors of variables: wff setvar class This definition is referenced by:  altxpeq1  31250  altxpeq2  31251  elaltxp  31252
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