Theorem f1ofo 5293

Description: A one-to-one onto function is an onto function. (Contributed by set.mm contributors, 28-Apr-2004.)

Assertion

Ref	Expression
f1ofo	|- (F:A-1-1-onto->B -> F:A-onto->B)

Proof of Theorem f1ofo

Step	Hyp	Ref	Expression
1		dff1o3 5292	. 2 |- (F:A-1-1-onto->B <-> (F:A-onto->B /\ Fun `'F))
2	1	simplbi 446	1 |- (F:A-1-1-onto->B -> F:A-onto->B)

Syntax hints:   -> wi 4  `'ccnv 4771  Fun wfun 4775  -onto->wfo 4779  -1-1-onto->wf1o 4780

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-ss 3259  df-f 4791  df-f1 4792  df-fo 4793  df-f1o 4794

This theorem is referenced by:  f1imacnv  5302  resin  5307  f1ococnv2  5309  fo00  5318  isoini  5497  bren  6030  enpw1  6062  enmap1lem5  6073  nenpw1pwlem2  6085  ncdisjun  6136  1cnc  6139  sbthlem3  6205  lenc  6223