New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  tpass Unicode version

Theorem tpass 3818
 Description: Split off the first element of an unordered triple. (Contributed by Mario Carneiro, 5-Jan-2016.)
Assertion
Ref Expression
tpass

Proof of Theorem tpass
StepHypRef Expression
1 df-tp 3743 . 2
2 tprot 3815 . 2
3 uncom 3408 . 2
41, 2, 33eqtr4i 2383 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1642   cun 3207  csn 3737  cpr 3738  ctp 3739 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3or 935  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-un 3214  df-sn 3741  df-pr 3742  df-tp 3743 This theorem is referenced by:  qdassr  3820
 Copyright terms: Public domain W3C validator