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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 8212 | . 2 ⊢ tpos 𝐹 = (𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) | |
2 | nftpos.1 | . . 3 ⊢ Ⅎ𝑥𝐹 | |
3 | nfcv 2902 | . . 3 ⊢ Ⅎ𝑥(𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦}) | |
4 | 2, 3 | nfco 5857 | . 2 ⊢ Ⅎ𝑥(𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ ∪ ◡{𝑦})) |
5 | 1, 4 | nfcxfr 2900 | 1 ⊢ Ⅎ𝑥tpos 𝐹 |
Colors of variables: wff setvar class |
Syntax hints: Ⅎwnfc 2882 Vcvv 3473 ∪ cun 3942 ∅c0 4318 {csn 4622 ∪ cuni 4901 ↦ cmpt 5224 × cxp 5667 ◡ccnv 5668 ∘ ccom 5673 tpos ctpos 8192 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-10 2137 ax-11 2154 ax-12 2171 ax-ext 2702 ax-sep 5292 ax-nul 5299 ax-pow 5356 ax-pr 5420 ax-un 7708 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-nf 1786 df-sb 2068 df-mo 2533 df-eu 2562 df-clab 2709 df-cleq 2723 df-clel 2809 df-nfc 2884 df-ne 2940 df-ral 3061 df-rex 3070 df-rab 3432 df-v 3475 df-dif 3947 df-un 3949 df-in 3951 df-ss 3961 df-nul 4319 df-if 4523 df-pw 4598 df-sn 4623 df-pr 4625 df-op 4629 df-uni 4902 df-br 5142 df-opab 5204 df-mpt 5225 df-id 5567 df-xp 5675 df-rel 5676 df-cnv 5677 df-co 5678 df-dm 5679 df-rn 5680 df-res 5681 df-ima 5682 df-iota 6484 df-fun 6534 df-fn 6535 df-fv 6540 df-tpos 8193 |
This theorem is referenced by: (None) |
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