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Definition df-tpos 7587
Description: Define the transposition of a function, which is a function 𝐺 = tpos 𝐹 satisfying 𝐺(𝑥, 𝑦) = 𝐹(𝑦, 𝑥). (Contributed by Mario Carneiro, 10-Sep-2015.)
Assertion
Ref Expression
df-tpos tpos 𝐹 = (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
Distinct variable group:   𝑥,𝐹

Detailed syntax breakdown of Definition df-tpos
StepHypRef Expression
1 cF . . 3 class 𝐹
21ctpos 7586 . 2 class tpos 𝐹
3 vx . . . 4 setvar 𝑥
41cdm 5311 . . . . . 6 class dom 𝐹
54ccnv 5310 . . . . 5 class dom 𝐹
6 c0 4116 . . . . . 6 class
76csn 4370 . . . . 5 class {∅}
85, 7cun 3767 . . . 4 class (dom 𝐹 ∪ {∅})
93cv 1636 . . . . . . 7 class 𝑥
109csn 4370 . . . . . 6 class {𝑥}
1110ccnv 5310 . . . . 5 class {𝑥}
1211cuni 4630 . . . 4 class {𝑥}
133, 8, 12cmpt 4923 . . 3 class (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥})
141, 13ccom 5315 . 2 class (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
152, 14wceq 1637 1 wff tpos 𝐹 = (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
Colors of variables: wff setvar class
This definition is referenced by:  tposss  7588  tposssxp  7591  brtpos2  7593  tposfun  7603  dftpos2  7604  dftpos4  7606
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