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| Mirrors > Home > MPE Home > Th. List > nftpos | Structured version Visualization version GIF version | ||
| Description: Hypothesis builder for transposition. (Contributed by Mario Carneiro, 10-Sep-2015.) |
| Ref | Expression |
|---|---|
| nftpos.1 | ⊢ Ⅎ𝑥𝐹 |
| Ref | Expression |
|---|---|
| nftpos | ⊢ Ⅎ𝑥tpos 𝐹 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | dftpos4 8270 | . 2 ⊢ tpos 𝐹 = (𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) | |
| 2 | nftpos.1 | . . 3 ⊢ Ⅎ𝑥𝐹 | |
| 3 | nfcv 2905 | . . 3 ⊢ Ⅎ𝑥(𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦}) | |
| 4 | 2, 3 | nfco 5876 | . 2 ⊢ Ⅎ𝑥(𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) |
| 5 | 1, 4 | nfcxfr 2903 | 1 ⊢ Ⅎ𝑥tpos 𝐹 |
| Colors of variables: wff setvar class |
| Syntax hints: Ⅎwnfc 2890 Vcvv 3480 ∪ cun 3949 ∅c0 4333 {csn 4626 ∪ cuni 4907 ↦ cmpt 5225 × cxp 5683 ◡ccnv 5684 ∘ ccom 5689 tpos ctpos 8250 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-10 2141 ax-11 2157 ax-12 2177 ax-ext 2708 ax-sep 5296 ax-nul 5306 ax-pow 5365 ax-pr 5432 ax-un 7755 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-nf 1784 df-sb 2065 df-mo 2540 df-eu 2569 df-clab 2715 df-cleq 2729 df-clel 2816 df-nfc 2892 df-ne 2941 df-ral 3062 df-rex 3071 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-in 3958 df-ss 3968 df-nul 4334 df-if 4526 df-pw 4602 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-opab 5206 df-mpt 5226 df-id 5578 df-xp 5691 df-rel 5692 df-cnv 5693 df-co 5694 df-dm 5695 df-rn 5696 df-res 5697 df-ima 5698 df-iota 6514 df-fun 6563 df-fn 6564 df-fv 6569 df-tpos 8251 |
| This theorem is referenced by: (None) |
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