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Theorem mptv 4332
 Description: Function with universal domain in maps-to notation. (Contributed by NM, 16-Aug-2013.)
Assertion
Ref Expression
mptv
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem mptv
StepHypRef Expression
1 df-mpt 4299 . 2
2 vex 2968 . . . 4
32biantrur 494 . . 3
43opabbii 4303 . 2
51, 4eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wa 360   wceq 1654   wcel 1728  cvv 2965  copab 4296   cmpt 4297 This theorem is referenced by:  df1st2  6469  df2nd2  6470  fsplit  6487  rankf  7756  cnmptid  17731 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 1628  ax-9 1669  ax-8 1690  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424 This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-clab 2430  df-cleq 2436  df-clel 2439  df-v 2967  df-opab 4298  df-mpt 4299
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