Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  f1od Structured version   Unicode version

Theorem f1od 6294
 Description: Describe an implicit one-to-one onto function. (Contributed by Mario Carneiro, 12-May-2014.)
Hypotheses
Ref Expression
f1od.1
f1od.2
f1od.3
f1od.4
Assertion
Ref Expression
f1od
Distinct variable groups:   ,,   ,,   ,   ,   ,,
Allowed substitution hints:   ()   ()   (,)   (,)   (,)

Proof of Theorem f1od
StepHypRef Expression
1 f1od.1 . . 3
2 f1od.2 . . 3
3 f1od.3 . . 3
4 f1od.4 . . 3
51, 2, 3, 4f1ocnvd 6293 . 2
65simpld 446 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725   cmpt 4266  ccnv 4877  wf1o 5453 This theorem is referenced by:  cnvf1o  6445  ixpsnf1o  7102  en2d  7143  pw2f1o  7213  seqf1olem1  11362 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-mpt 4268  df-id 4498  df-xp 4884  df-rel 4885  df-cnv 4886  df-co 4887  df-dm 4888  df-rn 4889  df-fun 5456  df-fn 5457  df-f 5458  df-f1 5459  df-fo 5460  df-f1o 5461
 Copyright terms: Public domain W3C validator