MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tposex Structured version   Visualization version   GIF version

Theorem tposex 7556
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 7536 . 2 (𝐹 ∈ V → tpos 𝐹 ∈ V)
31, 2ax-mp 5 1 tpos 𝐹 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2139  Vcvv 3340  tpos ctpos 7521
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1871  ax-4 1886  ax-5 1988  ax-6 2054  ax-7 2090  ax-8 2141  ax-9 2148  ax-10 2168  ax-11 2183  ax-12 2196  ax-13 2391  ax-ext 2740  ax-sep 4933  ax-nul 4941  ax-pow 4992  ax-pr 5055  ax-un 7115
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1635  df-ex 1854  df-nf 1859  df-sb 2047  df-eu 2611  df-mo 2612  df-clab 2747  df-cleq 2753  df-clel 2756  df-nfc 2891  df-ral 3055  df-rex 3056  df-rab 3059  df-v 3342  df-dif 3718  df-un 3720  df-in 3722  df-ss 3729  df-nul 4059  df-if 4231  df-pw 4304  df-sn 4322  df-pr 4324  df-op 4328  df-uni 4589  df-br 4805  df-opab 4865  df-mpt 4882  df-xp 5272  df-rel 5273  df-cnv 5274  df-co 5275  df-dm 5276  df-rn 5277  df-res 5278  df-ima 5279  df-tpos 7522
This theorem is referenced by:  oppchomfval  16595  oppccofval  16597  oppcmon  16619  yonedalem21  17134  yonedalem22  17139  oppgplusfval  17998  opprmulfval  18845
  Copyright terms: Public domain W3C validator