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Mirrors > Home > ILE Home > Th. List > nftpos | 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 6066 | . 2 ⊢ tpos 𝐹 = (𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) | |
2 | nftpos.1 | . . 3 ⊢ Ⅎ𝑥𝐹 | |
3 | nfcv 2235 | . . 3 ⊢ Ⅎ𝑥(𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦}) | |
4 | 2, 3 | nfco 4632 | . 2 ⊢ Ⅎ𝑥(𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) |
5 | 1, 4 | nfcxfr 2232 | 1 ⊢ Ⅎ𝑥tpos 𝐹 |
Colors of variables: wff set class |
Syntax hints: Ⅎwnfc 2222 Vcvv 2633 ∪ cun 3011 ∅c0 3302 {csn 3466 ∪ cuni 3675 ↦ cmpt 3921 × cxp 4465 ◡ccnv 4466 ∘ ccom 4471 tpos ctpos 6047 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-13 1456 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 ax-un 4284 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-sbc 2855 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-opab 3922 df-mpt 3923 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-rn 4478 df-res 4479 df-ima 4480 df-iota 5014 df-fun 5051 df-fn 5052 df-fv 5057 df-tpos 6048 |
This theorem is referenced by: (None) |
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