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Definition df-tpos 6146
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 6145 . 2 class tpos 𝐹
3 vx . . . 4 setvar 𝑥
41cdm 4543 . . . . . 6 class dom 𝐹
54ccnv 4542 . . . . 5 class dom 𝐹
6 c0 3364 . . . . . 6 class
76csn 3528 . . . . 5 class {∅}
85, 7cun 3070 . . . 4 class (dom 𝐹 ∪ {∅})
93cv 1331 . . . . . . 7 class 𝑥
109csn 3528 . . . . . 6 class {𝑥}
1110ccnv 4542 . . . . 5 class {𝑥}
1211cuni 3740 . . . 4 class {𝑥}
133, 8, 12cmpt 3993 . . 3 class (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥})
141, 13ccom 4547 . 2 class (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
152, 14wceq 1332 1 wff tpos 𝐹 = (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
Colors of variables: wff set class
This definition is referenced by:  tposss  6147  tposssxp  6150  brtpos2  6152  tposfun  6161  dftpos2  6162  dftpos4  6164
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