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Theorem nftpos 8228
Description: Hypothesis builder for transposition. (Contributed by Mario Carneiro, 10-Sep-2015.)
Hypothesis
Ref Expression
nftpos.1 𝑥𝐹
Assertion
Ref Expression
nftpos 𝑥tpos 𝐹

Proof of Theorem nftpos
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 dftpos4 8212 . 2 tpos 𝐹 = (𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦}))
2 nftpos.1 . . 3 𝑥𝐹
3 nfcv 2902 . . 3 𝑥(𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦})
42, 3nfco 5857 . 2 𝑥(𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦}))
51, 4nfcxfr 2900 1 𝑥tpos 𝐹
Colors of variables: wff setvar class
Syntax hints:  wnfc 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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