Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  dffv4g Unicode version

Theorem dffv4g 5206
 Description: The previous definition of function value, from before the operator was introduced. Although based on the idea embodied by Definition 10.2 of [Quine] p. 65 (see args 4724), this definition apparently does not appear in the literature. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
dffv4g
Distinct variable groups:   ,   ,   ,

Proof of Theorem dffv4g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dffv3g 5205 . 2
2 df-iota 4897 . . 3
3 abid2 2200 . . . . . 6
43eqeq1i 2089 . . . . 5
54abbii 2195 . . . 4
65unieqi 3619 . . 3
72, 6eqtri 2102 . 2
81, 7syl6eq 2130 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285   wcel 1434  cab 2068  csn 3406  cuni 3609  cima 4374  cio 4895  cfv 4932 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-eu 1945  df-mo 1946  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-sbc 2817  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-uni 3610  df-br 3794  df-opab 3848  df-xp 4377  df-cnv 4379  df-dm 4381  df-rn 4382  df-res 4383  df-ima 4384  df-iota 4897  df-fv 4940 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator