Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  dffun9 Structured version   Unicode version

Theorem dffun9 5473
 Description: Alternate definition of a function. (Contributed by NM, 28-Mar-2007.) (Revised by NM, 16-Jun-2017.)
Assertion
Ref Expression
dffun9
Distinct variable group:   ,,

Proof of Theorem dffun9
StepHypRef Expression
1 dffun7 5471 . 2
2 vex 2951 . . . . . . . 8
3 vex 2951 . . . . . . . 8
42, 3brelrn 5092 . . . . . . 7
54pm4.71ri 615 . . . . . 6
65mobii 2316 . . . . 5
7 df-rmo 2705 . . . . 5
86, 7bitr4i 244 . . . 4
98ralbii 2721 . . 3
109anbi2i 676 . 2
111, 10bitri 241 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359   wcel 1725  wmo 2281  wral 2697  wrmo 2700   class class class wbr 4204   cdm 4870   crn 4871   wrel 4875   wfun 5440 This theorem is referenced by:  brdom4  8400 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rmo 2705  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-br 4205  df-opab 4259  df-id 4490  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-fun 5448
 Copyright terms: Public domain W3C validator