MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  dffv4 Unicode version

Theorem dffv4 5868
Description: The previous definition of function value, from before the iota operator was introduced. Although based on the idea embodied by Definition 10.2 of [Quine] p. 65 (see args 5370), this definition apparently does not appear in the literature. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
dffv4
Distinct variable groups:   ,   ,

Proof of Theorem dffv4
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffv3 5867 . 2
2 df-iota 5556 . 2
3 abid2 2597 . . . . 5
43eqeq1i 2464 . . . 4
54abbii 2591 . . 3
65unieqi 4258 . 2
71, 2, 63eqtri 2490 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  {cab 2442  {csn 4029  U.cuni 4249  "cima 5007  iotacio 5554  `cfv 5593
This theorem is referenced by:  csbfv12gALTOLD  33621  csbfv12gALTVD  33699
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-8 1820  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pow 4630  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-iota 5556  df-fv 5601
  Copyright terms: Public domain W3C validator