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Theorem tposex 8241
Description: A transposition is a set. (Contributed by Mario Carneiro, 10-Sep-2015.)
Hypothesis
Ref Expression
tposex.1 𝐹 ∈ V
Assertion
Ref Expression
tposex tpos 𝐹 ∈ V

Proof of Theorem tposex
StepHypRef Expression
1 tposex.1 . 2 𝐹 ∈ V
2 tposexg 8221 . 2 (𝐹 ∈ V → tpos 𝐹 ∈ V)
31, 2ax-mp 5 1 tpos 𝐹 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2098  Vcvv 3466  tpos ctpos 8206
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pow 5354  ax-pr 5418  ax-un 7719
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-nf 1778  df-sb 2060  df-mo 2526  df-eu 2555  df-clab 2702  df-cleq 2716  df-clel 2802  df-nfc 2877  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-pw 4597  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-opab 5202  df-mpt 5223  df-xp 5673  df-rel 5674  df-cnv 5675  df-co 5676  df-dm 5677  df-rn 5678  df-res 5679  df-ima 5680  df-tpos 8207
This theorem is referenced by:  oppchomfval  17663  oppchomfvalOLD  17664  oppccofval  17666  oppcmon  17690  yonedalem21  18234  yonedalem22  18239  oppgplusfval  19260  opprmulfval  20234  opprabs  33092
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