ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nffo Structured version   Unicode version

Theorem nffo 5048
Description: Bound-variable hypothesis builder for an onto function. (Contributed by NM, 16-May-2004.)
Hypotheses
Ref Expression
nffo.1  F/_ F
nffo.2  F/_
nffo.3  F/_
Assertion
Ref Expression
nffo  F/  F : -onto->

Proof of Theorem nffo
StepHypRef Expression
1 df-fo 4851 . 2  F : -onto->  F  Fn  ran  F
2 nffo.1 . . . 4  F/_ F
3 nffo.2 . . . 4  F/_
42, 3nffn 4938 . . 3  F/  F  Fn
52nfrn 4522 . . . 4  F/_ ran  F
6 nffo.3 . . . 4  F/_
75, 6nfeq 2182 . . 3  F/ ran  F
84, 7nfan 1454 . 2  F/ F  Fn  ran  F
91, 8nfxfr 1360 1  F/  F : -onto->
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242   F/wnf 1346   F/_wnfc 2162   ran crn 4289    Fn wfn 4840   -onto->wfo 4843
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-3an 886  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-sn 3373  df-pr 3374  df-op 3376  df-br 3756  df-opab 3810  df-rel 4295  df-cnv 4296  df-co 4297  df-dm 4298  df-rn 4299  df-fun 4847  df-fn 4848  df-fo 4851
This theorem is referenced by:  nff1o  5067
  Copyright terms: Public domain W3C validator