MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-tpos Structured version   Visualization version   GIF version

Definition df-tpos 8211
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 8210 . 2 class tpos 𝐹
3 vx . . . 4 setvar 𝑥
41cdm 5677 . . . . . 6 class dom 𝐹
54ccnv 5676 . . . . 5 class dom 𝐹
6 c0 4323 . . . . . 6 class
76csn 4629 . . . . 5 class {∅}
85, 7cun 3947 . . . 4 class (dom 𝐹 ∪ {∅})
93cv 1541 . . . . . . 7 class 𝑥
109csn 4629 . . . . . 6 class {𝑥}
1110ccnv 5676 . . . . 5 class {𝑥}
1211cuni 4909 . . . 4 class {𝑥}
133, 8, 12cmpt 5232 . . 3 class (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥})
141, 13ccom 5681 . 2 class (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
152, 14wceq 1542 1 wff tpos 𝐹 = (𝐹 ∘ (𝑥 ∈ (dom 𝐹 ∪ {∅}) ↦ {𝑥}))
Colors of variables: wff setvar class
This definition is referenced by:  tposss  8212  tposssxp  8215  brtpos2  8217  tposfun  8227  dftpos2  8228  dftpos4  8230
  Copyright terms: Public domain W3C validator