Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  mpt2eq123i Structured version   Unicode version

Theorem mpt2eq123i 6341
 Description: An equality inference for the maps to notation. (Contributed by NM, 15-Jul-2013.)
Hypotheses
Ref Expression
mpt2eq123i.1
mpt2eq123i.2
mpt2eq123i.3
Assertion
Ref Expression
mpt2eq123i

Proof of Theorem mpt2eq123i
StepHypRef Expression
1 mpt2eq123i.1 . . . 4
21a1i 11 . . 3
3 mpt2eq123i.2 . . . 4
43a1i 11 . . 3
5 mpt2eq123i.3 . . . 4
65a1i 11 . . 3
72, 4, 6mpt2eq123dv 6340 . 2
87trud 1414 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1405   wtru 1406   cmpt2 6280 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-oprab 6282  df-mpt2 6283 This theorem is referenced by:  ofmres  6780  seqval  12162  dprdvalOLD  17356  oppgtmd  20888  sdc  31519  tgrpset  33764  mendvscafval  35503
 Copyright terms: Public domain W3C validator