Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  mpt2v Structured version   Unicode version

Theorem mpt2v 6166
 Description: Operation with universal domain in maps-to notation. (Contributed by NM, 16-Aug-2013.)
Assertion
Ref Expression
mpt2v
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   (,)

Proof of Theorem mpt2v
StepHypRef Expression
1 df-mpt2 6089 . 2
2 vex 2961 . . . . 5
3 vex 2961 . . . . 5
42, 3pm3.2i 443 . . . 4
54biantrur 494 . . 3
65oprabbii 6132 . 2
71, 6eqtr4i 2461 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1653   wcel 1726  cvv 2958  coprab 6085   cmpt2 6086 This theorem is referenced by:  1st2val  6375  2nd2val  6376 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-v 2960  df-oprab 6088  df-mpt2 6089
 Copyright terms: Public domain W3C validator