Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  tz6.12-1 Structured version   Unicode version

Theorem tz6.12-1 5865
 Description: Function value. Theorem 6.12(1) of [TakeutiZaring] p. 27. (Contributed by NM, 30-Apr-2004.)
Assertion
Ref Expression
tz6.12-1
Distinct variable groups:   ,   ,

Proof of Theorem tz6.12-1
StepHypRef Expression
1 df-fv 5577 . 2
2 iota1 5547 . . 3
32biimpac 484 . 2
41, 3syl5eq 2455 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 367   wceq 1405  weu 2238   class class class wbr 4395  cio 5531  cfv 5569 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-rex 2760  df-v 3061  df-sbc 3278  df-un 3419  df-sn 3973  df-pr 3975  df-uni 4192  df-iota 5533  df-fv 5577 This theorem is referenced by:  tz6.12  5866  tz6.12c  5868  funbrfv  5887
 Copyright terms: Public domain W3C validator