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

Theorem addex 10368
 Description: The addition operation is a set. (Contributed by NM, 19-Oct-2004.) (Revised by Mario Carneiro, 17-Nov-2014.)
Assertion
Ref Expression
addex

Proof of Theorem addex
StepHypRef Expression
1 ax-addf 8832 . 2
2 cnex 8834 . . 3
32, 2xpex 4817 . 2
4 fex2 5417 . 2
51, 3, 2, 4mp3an 1277 1
 Colors of variables: wff set class Syntax hints:   wcel 1696  cvv 2801   cxp 4703  wf 5267  cc 8751   caddc 8756 This theorem is referenced by:  cnaddablx  15174  cnaddabl  15175  zaddablx  15176  cnfldadd  16400  cnnvg  21262  cnnvs  21265  cncph  21413  zintdom  25541  cnaddcom  29783 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-13 1698  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pow 4204  ax-pr 4230  ax-un 4528  ax-cnex 8809  ax-addf 8832 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-pw 3640  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-xp 4711  df-rel 4712  df-cnv 4713  df-dm 4715  df-rn 4716  df-fun 5273  df-fn 5274  df-f 5275
 Copyright terms: Public domain W3C validator