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

Theorem ofreq 6308
 Description: Equality theorem for function relation. (Contributed by Mario Carneiro, 28-Jul-2014.)
Assertion
Ref Expression
ofreq

Proof of Theorem ofreq
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 breq 4214 . . . 4
21ralbidv 2725 . . 3
32opabbidv 4271 . 2
4 df-ofr 6306 . 2
5 df-ofr 6306 . 2
63, 4, 53eqtr4g 2493 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652  wral 2705   cin 3319   class class class wbr 4212  copab 4265   cdm 4878  cfv 5454   cofr 6304 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-ral 2710  df-br 4213  df-opab 4267  df-ofr 6306
 Copyright terms: Public domain W3C validator