ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  fofn GIF version

Theorem fofn 5347
Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008.)
Assertion
Ref Expression
fofn (𝐹:𝐴onto𝐵𝐹 Fn 𝐴)

Proof of Theorem fofn
StepHypRef Expression
1 fof 5345 . 2 (𝐹:𝐴onto𝐵𝐹:𝐴𝐵)
2 ffn 5272 . 2 (𝐹:𝐴𝐵𝐹 Fn 𝐴)
31, 2syl 14 1 (𝐹:𝐴onto𝐵𝐹 Fn 𝐴)
Colors of variables: wff set class
Syntax hints:  wi 4   Fn wfn 5118  wf 5119  ontowfo 5121
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-in 3077  df-ss 3084  df-f 5127  df-fo 5129
This theorem is referenced by:  fodmrnu  5353  foun  5386  fo00  5403  foima2  5653  cbvfo  5686  cbvexfo  5687  foeqcnvco  5691  1stcof  6061  2ndcof  6062  1stexg  6065  2ndexg  6066  df1st2  6116  df2nd2  6117  1stconst  6118  2ndconst  6119  fidcenumlemrks  6841  fidcenumlemr  6843  ctm  6994  suplocexprlemell  7528  ennnfonelemhf1o  11933  ennnfonelemrn  11939  upxp  12451  uptx  12453  cnmpt1st  12467  cnmpt2nd  12468
  Copyright terms: Public domain W3C validator