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Theorem nftpos 7944
 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 7928 . 2 tpos 𝐹 = (𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦}))
2 nftpos.1 . . 3 𝑥𝐹
3 nfcv 2920 . . 3 𝑥(𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦})
42, 3nfco 5712 . 2 𝑥(𝐹 ∘ (𝑦 ∈ ((V × V) ∪ {∅}) ↦ {𝑦}))
51, 4nfcxfr 2918 1 𝑥tpos 𝐹
 Colors of variables: wff setvar class Syntax hints:  Ⅎwnfc 2900  Vcvv 3410   ∪ cun 3859  ∅c0 4228  {csn 4526  ∪ cuni 4802   ↦ cmpt 5117   × cxp 5527  ◡ccnv 5528   ∘ ccom 5533  tpos ctpos 7908 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2114  ax-9 2122  ax-10 2143  ax-11 2159  ax-12 2176  ax-ext 2730  ax-sep 5174  ax-nul 5181  ax-pow 5239  ax-pr 5303  ax-un 7466 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1087  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2071  df-mo 2558  df-eu 2589  df-clab 2737  df-cleq 2751  df-clel 2831  df-nfc 2902  df-ne 2953  df-ral 3076  df-rex 3077  df-rab 3080  df-v 3412  df-sbc 3700  df-dif 3864  df-un 3866  df-in 3868  df-ss 3878  df-nul 4229  df-if 4425  df-pw 4500  df-sn 4527  df-pr 4529  df-op 4533  df-uni 4803  df-br 5038  df-opab 5100  df-mpt 5118  df-id 5435  df-xp 5535  df-rel 5536  df-cnv 5537  df-co 5538  df-dm 5539  df-rn 5540  df-res 5541  df-ima 5542  df-iota 6300  df-fun 6343  df-fn 6344  df-fv 6349  df-tpos 7909 This theorem is referenced by: (None)
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