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Definition df-tpos 5782
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 5781 . 2 class tpos 𝐹
3 vx . . . 4 setvar x
41cdm 4272 . . . . . 6 class dom 𝐹
54ccnv 4271 . . . . 5 class dom 𝐹
6 c0 3201 . . . . . 6 class
76csn 3350 . . . . 5 class {∅}
85, 7cun 2892 . . . 4 class (dom 𝐹 ∪ {∅})
93cv 1227 . . . . . . 7 class x
109csn 3350 . . . . . 6 class {x}
1110ccnv 4271 . . . . 5 class {x}
1211cuni 3554 . . . 4 class {x}
133, 8, 12cmpt 3792 . . 3 class (x (dom 𝐹 ∪ {∅}) ↦ {x})
141, 13ccom 4276 . 2 class (𝐹 ∘ (x (dom 𝐹 ∪ {∅}) ↦ {x}))
152, 14wceq 1228 1 wff tpos 𝐹 = (𝐹 ∘ (x (dom 𝐹 ∪ {∅}) ↦ {x}))
Colors of variables: wff set class
This definition is referenced by:  tposss  5783  tposssxp  5786  brtpos2  5788  tposfun  5797  dftpos2  5798  dftpos4  5800
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