MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  tz6.12 Unicode version

Theorem tz6.12 5888
Description: Function value. Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 10-Jul-1994.)
Assertion
Ref Expression
tz6.12
Distinct variable groups:   ,   ,

Proof of Theorem tz6.12
StepHypRef Expression
1 df-br 4453 . 2
21eubii 2306 . 2
3 tz6.12-1 5887 . 2
41, 2, 3syl2anbr 480 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  e.wcel 1818  E!weu 2282  <.cop 4035   class class class wbr 4452  `cfv 5593
This theorem is referenced by:  tz6.12f  5889  dfac5lem5  8529  tz6.12-afv  32258
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rex 2813  df-v 3111  df-sbc 3328  df-un 3480  df-sn 4030  df-pr 4032  df-uni 4250  df-br 4453  df-iota 5556  df-fv 5601
  Copyright terms: Public domain W3C validator